{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-form-validity-0001","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"36add127eec5c4f1f43feafb3e52e2293230880bc1536f1dc66e72241472c9e5","family_id":"qf-linear-equation-form-validity","seed":20260928,"semantic_template":"qf-linear-equation-form-validity/{\"a\":0,\"b\":-12,\"domain\":\"rationals\",\"operation\":\"form_validity\"}"},"fields":{"title":"Validity of a Linear-Equation Form","stem":"Over the rational numbers, consider 0x+(-12)=0. Under this MKO, is it a linear equation in one variable?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"a=0, so this is a degenerate constant equation rather than a linear equation in one variable."},"skills":["linear coefficient","equation form"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-form-validity-0002","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"593a81830a9676943410f94de2121fe9f05e9229bced4f33e91e3e8bc8ab856a","family_id":"qf-linear-equation-form-validity","seed":20260929,"semantic_template":"qf-linear-equation-form-validity/{\"a\":-3,\"b\":-11,\"domain\":\"rationals\",\"operation\":\"form_validity\"}"},"fields":{"title":"Validity of a Linear-Equation Form","stem":"Over the rational numbers, consider -3x+(-11)=0. Under this MKO, is it a linear equation in one variable?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"a=-3≠0, so this is a linear equation in one variable under the MKO definition."},"skills":["linear coefficient","equation form"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-form-validity-0003","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fa4bb88d16c236ebb72a82e2896157760b07f0fab1bc41300e14bfde5d9fc858","family_id":"qf-linear-equation-form-validity","seed":20260930,"semantic_template":"qf-linear-equation-form-validity/{\"a\":-2,\"b\":-10,\"domain\":\"rationals\",\"operation\":\"form_validity\"}"},"fields":{"title":"Validity of a Linear-Equation Form","stem":"Over the rational numbers, consider -2x+(-10)=0. Under this MKO, is it a linear equation in one variable?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"a=-2≠0, so this is a linear equation in one variable under the MKO definition."},"skills":["linear coefficient","equation form"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-form-validity-0004","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6500e6782be175f3b6e832d442e3f0e4a005e57c86827aa0f14e2ccb486a2b0a","family_id":"qf-linear-equation-form-validity","seed":20260931,"semantic_template":"qf-linear-equation-form-validity/{\"a\":-1,\"b\":-9,\"domain\":\"rationals\",\"operation\":\"form_validity\"}"},"fields":{"title":"Validity of a Linear-Equation Form","stem":"Over the rational numbers, consider -1x+(-9)=0. Under this MKO, is it a linear equation in one variable?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"a=-1≠0, so this is a linear equation in one variable under the MKO definition."},"skills":["linear coefficient","equation form"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-form-validity-0005","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ed846438e63f90bcab59034cbfad2ca8189834d9aebc88ec53465fd6e53da4a5","family_id":"qf-linear-equation-form-validity","seed":20260932,"semantic_template":"qf-linear-equation-form-validity/{\"a\":1,\"b\":-8,\"domain\":\"rationals\",\"operation\":\"form_validity\"}"},"fields":{"title":"Validity of a Linear-Equation Form","stem":"Over the rational numbers, consider 1x+(-8)=0. Under this MKO, is it a linear equation in one variable?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"a=1≠0, so this is a linear equation in one variable under the MKO definition."},"skills":["linear coefficient","equation form"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-form-validity-0006","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"42d38ceefd9828384c48cdba2ed32869fb4315f2db80d9b86744fd78f491835e","family_id":"qf-linear-equation-form-validity","seed":20260933,"semantic_template":"qf-linear-equation-form-validity/{\"a\":0,\"b\":-7,\"domain\":\"rationals\",\"operation\":\"form_validity\"}"},"fields":{"title":"Validity of a Linear-Equation Form","stem":"Over the rational numbers, consider 0x+(-7)=0. Under this MKO, is it a linear equation in one variable?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"a=0, so this is a degenerate constant equation rather than a linear equation in one variable."},"skills":["linear coefficient","equation form"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-form-validity-0007","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"12c7fb146f0610590ace7b3b56529bddbf4b33d00c6f24b8dc7e31fdb0df543a","family_id":"qf-linear-equation-form-validity","seed":20260934,"semantic_template":"qf-linear-equation-form-validity/{\"a\":2,\"b\":-6,\"domain\":\"rationals\",\"operation\":\"form_validity\"}"},"fields":{"title":"Validity of a Linear-Equation Form","stem":"Over the rational numbers, consider 2x+(-6)=0. Under this MKO, is it a linear equation in one variable?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"a=2≠0, so this is a linear equation in one variable under the MKO definition."},"skills":["linear coefficient","equation form"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-form-validity-0008","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a777b98b6b4207137ce3f8fbd388db09f831ad6c0c91d63d01f2e1df127eeea4","family_id":"qf-linear-equation-form-validity","seed":20260935,"semantic_template":"qf-linear-equation-form-validity/{\"a\":3,\"b\":-5,\"domain\":\"rationals\",\"operation\":\"form_validity\"}"},"fields":{"title":"Validity of a Linear-Equation Form","stem":"Over the rational numbers, consider 3x+(-5)=0. Under this MKO, is it a linear equation in one variable?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"a=3≠0, so this is a linear equation in one variable under the MKO definition."},"skills":["linear coefficient","equation form"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-form-validity-0009","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"155dee231f0dfb7780d84ddded7dd543a0d7c58a4be35949c29fd1cdba48d18d","family_id":"qf-linear-equation-form-validity","seed":20260936,"semantic_template":"qf-linear-equation-form-validity/{\"a\":4,\"b\":-4,\"domain\":\"rationals\",\"operation\":\"form_validity\"}"},"fields":{"title":"Validity of a Linear-Equation Form","stem":"Over the rational numbers, consider 4x+(-4)=0. Under this MKO, is it a linear equation in one variable?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"a=4≠0, so this is a linear equation in one variable under the MKO definition."},"skills":["linear coefficient","equation form"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-form-validity-0010","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ca869a38df97ff78d9f62162732d69ccfee8dc10e890fe145772a5084c9b321c","family_id":"qf-linear-equation-form-validity","seed":20260937,"semantic_template":"qf-linear-equation-form-validity/{\"a\":-4,\"b\":-3,\"domain\":\"rationals\",\"operation\":\"form_validity\"}"},"fields":{"title":"Validity of a Linear-Equation Form","stem":"Over the rational numbers, consider -4x+(-3)=0. Under this MKO, is it a linear equation in one variable?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"a=-4≠0, so this is a linear equation in one variable under the MKO definition."},"skills":["linear coefficient","equation form"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-form-validity-0011","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"87e129c9e59b794f760def597d24caf32015ffa580a2acba8bca038f370c3353","family_id":"qf-linear-equation-form-validity","seed":20260938,"semantic_template":"qf-linear-equation-form-validity/{\"a\":0,\"b\":-2,\"domain\":\"rationals\",\"operation\":\"form_validity\"}"},"fields":{"title":"Validity of a Linear-Equation Form","stem":"Over the rational numbers, consider 0x+(-2)=0. Under this MKO, is it a linear equation in one variable?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"a=0, so this is a degenerate constant equation rather than a linear equation in one variable."},"skills":["linear coefficient","equation form"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-form-validity-0012","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b8965047ede53076bbececb50a9a402e83d7f65efee6a3a6c08bdb8209f9436c","family_id":"qf-linear-equation-form-validity","seed":20260939,"semantic_template":"qf-linear-equation-form-validity/{\"a\":-2,\"b\":-1,\"domain\":\"rationals\",\"operation\":\"form_validity\"}"},"fields":{"title":"Validity of a Linear-Equation Form","stem":"Over the rational numbers, consider -2x+(-1)=0. Under this MKO, is it a linear equation in one variable?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"a=-2≠0, so this is a linear equation in one variable under the MKO definition."},"skills":["linear coefficient","equation form"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-form-validity-0013","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"28c65472b4197a7a970bb141b00b26e3c210c9b839c7b7a79614683ac0967cd0","family_id":"qf-linear-equation-form-validity","seed":20260940,"semantic_template":"qf-linear-equation-form-validity/{\"a\":-1,\"b\":0,\"domain\":\"rationals\",\"operation\":\"form_validity\"}"},"fields":{"title":"Validity of a Linear-Equation Form","stem":"Over the rational numbers, consider -1x+(0)=0. Under this MKO, is it a linear equation in one variable?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"a=-1≠0, so this is a linear equation in one variable under the MKO definition."},"skills":["linear coefficient","equation form"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-form-validity-0014","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"77ffe93fb75bdf95b4d0e95ddd5ea3115d32a5ba71dea72cca7ad7196dcb1a7a","family_id":"qf-linear-equation-form-validity","seed":20260941,"semantic_template":"qf-linear-equation-form-validity/{\"a\":1,\"b\":1,\"domain\":\"rationals\",\"operation\":\"form_validity\"}"},"fields":{"title":"Validity of a Linear-Equation Form","stem":"Over the rational numbers, consider 1x+(1)=0. Under this MKO, is it a linear equation in one variable?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"a=1≠0, so this is a linear equation in one variable under the MKO definition."},"skills":["linear coefficient","equation form"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-form-validity-0015","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4dd0f6666c45b80172a73f39f34ccd51666d6da8bb269df7bfef07e93e9a0d31","family_id":"qf-linear-equation-form-validity","seed":20260942,"semantic_template":"qf-linear-equation-form-validity/{\"a\":1,\"b\":2,\"domain\":\"rationals\",\"operation\":\"form_validity\"}"},"fields":{"title":"Validity of a Linear-Equation Form","stem":"Over the rational numbers, consider 1x+(2)=0. Under this MKO, is it a linear equation in one variable?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"a=1≠0, so this is a linear equation in one variable under the MKO definition."},"skills":["linear coefficient","equation form"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-form-validity-0016","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"cc3361eb3a539bd5020b69e90240a236f5c444bb46ab80ee4a1d22104b4fc27d","family_id":"qf-linear-equation-form-validity","seed":20260943,"semantic_template":"qf-linear-equation-form-validity/{\"a\":0,\"b\":3,\"domain\":\"rationals\",\"operation\":\"form_validity\"}"},"fields":{"title":"Validity of a Linear-Equation Form","stem":"Over the rational numbers, consider 0x+(3)=0. Under this MKO, is it a linear equation in one variable?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"a=0, so this is a degenerate constant equation rather than a linear equation in one variable."},"skills":["linear coefficient","equation form"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-form-validity-0017","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c047bdde1a0968d3cc9cda58eeaa70b239af1879b0273186d6aacba7115fb914","family_id":"qf-linear-equation-form-validity","seed":20260944,"semantic_template":"qf-linear-equation-form-validity/{\"a\":3,\"b\":4,\"domain\":\"rationals\",\"operation\":\"form_validity\"}"},"fields":{"title":"Validity of a Linear-Equation Form","stem":"Over the rational numbers, consider 3x+(4)=0. Under this MKO, is it a linear equation in one variable?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"a=3≠0, so this is a linear equation in one variable under the MKO definition."},"skills":["linear coefficient","equation form"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-form-validity-0018","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"04766c5c07dc6b3991734b527ead3aef8019f233476d5820213977666044ab74","family_id":"qf-linear-equation-form-validity","seed":20260945,"semantic_template":"qf-linear-equation-form-validity/{\"a\":4,\"b\":5,\"domain\":\"rationals\",\"operation\":\"form_validity\"}"},"fields":{"title":"Validity of a Linear-Equation Form","stem":"Over the rational numbers, consider 4x+(5)=0. Under this MKO, is it a linear equation in one variable?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"a=4≠0, so this is a linear equation in one variable under the MKO definition."},"skills":["linear coefficient","equation form"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-form-validity-0019","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a1279617a0db69ef88744fb20b086091808b9fed2454b533086c8e81a04da7cc","family_id":"qf-linear-equation-form-validity","seed":20260946,"semantic_template":"qf-linear-equation-form-validity/{\"a\":-4,\"b\":6,\"domain\":\"rationals\",\"operation\":\"form_validity\"}"},"fields":{"title":"Validity of a Linear-Equation Form","stem":"Over the rational numbers, consider -4x+(6)=0. Under this MKO, is it a linear equation in one variable?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"a=-4≠0, so this is a linear equation in one variable under the MKO definition."},"skills":["linear coefficient","equation form"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-form-validity-0020","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"00d52794471aca620587ec86b6bb66753eb658cd21e5c31e6e14b81ecd1063a3","family_id":"qf-linear-equation-form-validity","seed":20260947,"semantic_template":"qf-linear-equation-form-validity/{\"a\":-3,\"b\":7,\"domain\":\"rationals\",\"operation\":\"form_validity\"}"},"fields":{"title":"Validity of a Linear-Equation Form","stem":"Over the rational numbers, consider -3x+(7)=0. Under this MKO, is it a linear equation in one variable?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"a=-3≠0, so this is a linear equation in one variable under the MKO definition."},"skills":["linear coefficient","equation form"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-form-validity-0021","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"92c58b66d5444d9b8f12263e7717f39bbb158f81ba411fd0ba9969bdff47591a","family_id":"qf-linear-equation-form-validity","seed":20260948,"semantic_template":"qf-linear-equation-form-validity/{\"a\":0,\"b\":8,\"domain\":\"rationals\",\"operation\":\"form_validity\"}"},"fields":{"title":"Validity of a Linear-Equation Form","stem":"Over the rational numbers, consider 0x+(8)=0. Under this MKO, is it a linear equation in one variable?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"a=0, so this is a degenerate constant equation rather than a linear equation in one variable."},"skills":["linear coefficient","equation form"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-form-validity-0022","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"380a5c4d8b4241fa6432b604b52b8e03cff8426b3b76c6426028487fb6852b30","family_id":"qf-linear-equation-form-validity","seed":20260949,"semantic_template":"qf-linear-equation-form-validity/{\"a\":-1,\"b\":9,\"domain\":\"rationals\",\"operation\":\"form_validity\"}"},"fields":{"title":"Validity of a Linear-Equation Form","stem":"Over the rational numbers, consider -1x+(9)=0. Under this MKO, is it a linear equation in one variable?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"a=-1≠0, so this is a linear equation in one variable under the MKO definition."},"skills":["linear coefficient","equation form"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-form-validity-0023","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b7ecc1b53fad045a7260e10dfac795ff7b30fd2b05305037d3e93a3fae9ea07e","family_id":"qf-linear-equation-form-validity","seed":20260950,"semantic_template":"qf-linear-equation-form-validity/{\"a\":1,\"b\":10,\"domain\":\"rationals\",\"operation\":\"form_validity\"}"},"fields":{"title":"Validity of a Linear-Equation Form","stem":"Over the rational numbers, consider 1x+(10)=0. Under this MKO, is it a linear equation in one variable?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"a=1≠0, so this is a linear equation in one variable under the MKO definition."},"skills":["linear coefficient","equation form"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-form-validity-0024","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"87a84862dbfef9930c794525319f38bb7c61e9d8b86fc6e932944818da47da84","family_id":"qf-linear-equation-form-validity","seed":20260951,"semantic_template":"qf-linear-equation-form-validity/{\"a\":1,\"b\":11,\"domain\":\"rationals\",\"operation\":\"form_validity\"}"},"fields":{"title":"Validity of a Linear-Equation Form","stem":"Over the rational numbers, consider 1x+(11)=0. Under this MKO, is it a linear equation in one variable?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"a=1≠0, so this is a linear equation in one variable under the MKO definition."},"skills":["linear coefficient","equation form"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-form-validity-0025","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"21b19b34840451b76342e34f225540a60cfad14dbc36c6ad7082b07fa6d2dfe7","family_id":"qf-linear-equation-form-validity","seed":20260952,"semantic_template":"qf-linear-equation-form-validity/{\"a\":2,\"b\":12,\"domain\":\"rationals\",\"operation\":\"form_validity\"}"},"fields":{"title":"Validity of a Linear-Equation Form","stem":"Over the rational numbers, consider 2x+(12)=0. Under this MKO, is it a linear equation in one variable?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"a=2≠0, so this is a linear equation in one variable under the MKO definition."},"skills":["linear coefficient","equation form"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-exact-solve-0001","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b10ff83dcf7bb89f4d0ebaeb6d5e4577e6a3b25cd701fc76e4009b549627f515","family_id":"qf-linear-equation-exact-solve","seed":20261028,"semantic_template":"qf-linear-equation-exact-solve/{\"a\":-5,\"b\":-15,\"domain\":\"rationals\",\"operation\":\"exact_solve\"}"},"fields":{"title":"Exact Solution of a Linear Equation","stem":"Solve -5x+(-15)=0 exactly over the rational numbers; a=-5 is explicitly nonzero.","answer":{"kind":"short_text","value":"-3","explanation":"x=−(-15)/-5=-3; the result is reduced by the gcd to a canonical rational with a positive denominator."},"skills":["rational numbers","canonical fraction"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-exact-solve-0002","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"94ca7d0b994962b78f0f44a5056deddb09c18848a5f2235829f3c612d3775a11","family_id":"qf-linear-equation-exact-solve","seed":20261029,"semantic_template":"qf-linear-equation-exact-solve/{\"a\":-4,\"b\":-8,\"domain\":\"rationals\",\"operation\":\"exact_solve\"}"},"fields":{"title":"Exact Solution of a Linear Equation","stem":"Solve -4x+(-8)=0 exactly over the rational numbers; a=-4 is explicitly nonzero.","answer":{"kind":"short_text","value":"-2","explanation":"x=−(-8)/-4=-2; the result is reduced by the gcd to a canonical rational with a positive denominator."},"skills":["rational numbers","canonical fraction"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-exact-solve-0003","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6bf7d91007e2bd9f6375f78be76d9d4d0d0dac72aa464878cfb31093fff342e4","family_id":"qf-linear-equation-exact-solve","seed":20261030,"semantic_template":"qf-linear-equation-exact-solve/{\"a\":-3,\"b\":-1,\"domain\":\"rationals\",\"operation\":\"exact_solve\"}"},"fields":{"title":"Exact Solution of a Linear Equation","stem":"Solve -3x+(-1)=0 exactly over the rational numbers; a=-3 is explicitly nonzero.","answer":{"kind":"short_text","value":"-1/3","explanation":"x=−(-1)/-3=-1/3; the result is reduced by the gcd to a canonical rational with a positive denominator."},"skills":["rational numbers","canonical fraction"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-exact-solve-0004","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"cb22fef4c873a3a80185532b7fa98b449dae4066b851c5ca768b0c18c22fbe29","family_id":"qf-linear-equation-exact-solve","seed":20261031,"semantic_template":"qf-linear-equation-exact-solve/{\"a\":-2,\"b\":6,\"domain\":\"rationals\",\"operation\":\"exact_solve\"}"},"fields":{"title":"Exact Solution of a Linear Equation","stem":"Solve -2x+(6)=0 exactly over the rational numbers; a=-2 is explicitly nonzero.","answer":{"kind":"short_text","value":"3","explanation":"x=−(6)/-2=3; the result is reduced by the gcd to a canonical rational with a positive denominator."},"skills":["rational numbers","canonical fraction"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-exact-solve-0005","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a5cbcee96fa853f3f1ba998000701fc6fe5beb42ddf308e45b2d56769cf91877","family_id":"qf-linear-equation-exact-solve","seed":20261032,"semantic_template":"qf-linear-equation-exact-solve/{\"a\":-1,\"b\":13,\"domain\":\"rationals\",\"operation\":\"exact_solve\"}"},"fields":{"title":"Exact Solution of a Linear Equation","stem":"Solve -1x+(13)=0 exactly over the rational numbers; a=-1 is explicitly nonzero.","answer":{"kind":"short_text","value":"13","explanation":"x=−(13)/-1=13; the result is reduced by the gcd to a canonical rational with a positive denominator."},"skills":["rational numbers","canonical fraction"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-exact-solve-0006","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e129435cac83dbb3a444642d5d1d5ca206988b2e6a63d14f63ff35fb02a8402f","family_id":"qf-linear-equation-exact-solve","seed":20261033,"semantic_template":"qf-linear-equation-exact-solve/{\"a\":1,\"b\":-11,\"domain\":\"rationals\",\"operation\":\"exact_solve\"}"},"fields":{"title":"Exact Solution of a Linear Equation","stem":"Solve 1x+(-11)=0 exactly over the rational numbers; a=1 is explicitly nonzero.","answer":{"kind":"short_text","value":"11","explanation":"x=−(-11)/1=11; the result is reduced by the gcd to a canonical rational with a positive denominator."},"skills":["rational numbers","canonical fraction"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-exact-solve-0007","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3c7c8ad828b954e79604ddaf8c31c17677a90c354a1da2ad13328d1f1aa406a6","family_id":"qf-linear-equation-exact-solve","seed":20261034,"semantic_template":"qf-linear-equation-exact-solve/{\"a\":1,\"b\":-4,\"domain\":\"rationals\",\"operation\":\"exact_solve\"}"},"fields":{"title":"Exact Solution of a Linear Equation","stem":"Solve 1x+(-4)=0 exactly over the rational numbers; a=1 is explicitly nonzero.","answer":{"kind":"short_text","value":"4","explanation":"x=−(-4)/1=4; the result is reduced by the gcd to a canonical rational with a positive denominator."},"skills":["rational numbers","canonical fraction"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-exact-solve-0008","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7624f5b6c092b3b42e2d0326f1a96dabd8304a4bc3be12db78beb9645203184d","family_id":"qf-linear-equation-exact-solve","seed":20261035,"semantic_template":"qf-linear-equation-exact-solve/{\"a\":2,\"b\":3,\"domain\":\"rationals\",\"operation\":\"exact_solve\"}"},"fields":{"title":"Exact Solution of a Linear Equation","stem":"Solve 2x+(3)=0 exactly over the rational numbers; a=2 is explicitly nonzero.","answer":{"kind":"short_text","value":"-3/2","explanation":"x=−(3)/2=-3/2; the result is reduced by the gcd to a canonical rational with a positive denominator."},"skills":["rational numbers","canonical fraction"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-exact-solve-0009","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"baf444414503274f6abf17e482e248a85ffe2db94f3098eff428aa751a36f001","family_id":"qf-linear-equation-exact-solve","seed":20261036,"semantic_template":"qf-linear-equation-exact-solve/{\"a\":3,\"b\":10,\"domain\":\"rationals\",\"operation\":\"exact_solve\"}"},"fields":{"title":"Exact Solution of a Linear Equation","stem":"Solve 3x+(10)=0 exactly over the rational numbers; a=3 is explicitly nonzero.","answer":{"kind":"short_text","value":"-10/3","explanation":"x=−(10)/3=-10/3; the result is reduced by the gcd to a canonical rational with a positive denominator."},"skills":["rational numbers","canonical fraction"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-exact-solve-0010","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d2356c1ecc314cd0cbaae77a94d84bc2086daa5d9ef4162aefe94e88e84c1698","family_id":"qf-linear-equation-exact-solve","seed":20261037,"semantic_template":"qf-linear-equation-exact-solve/{\"a\":4,\"b\":-14,\"domain\":\"rationals\",\"operation\":\"exact_solve\"}"},"fields":{"title":"Exact Solution of a Linear Equation","stem":"Solve 4x+(-14)=0 exactly over the rational numbers; a=4 is explicitly nonzero.","answer":{"kind":"short_text","value":"7/2","explanation":"x=−(-14)/4=7/2; the result is reduced by the gcd to a canonical rational with a positive denominator."},"skills":["rational numbers","canonical fraction"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-exact-solve-0011","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f69b61f6159deb77503ec3cc7ddcb73a72fb98544a09a82bfd6a003873d4d247","family_id":"qf-linear-equation-exact-solve","seed":20261038,"semantic_template":"qf-linear-equation-exact-solve/{\"a\":5,\"b\":-7,\"domain\":\"rationals\",\"operation\":\"exact_solve\"}"},"fields":{"title":"Exact Solution of a Linear Equation","stem":"Solve 5x+(-7)=0 exactly over the rational numbers; a=5 is explicitly nonzero.","answer":{"kind":"short_text","value":"7/5","explanation":"x=−(-7)/5=7/5; the result is reduced by the gcd to a canonical rational with a positive denominator."},"skills":["rational numbers","canonical fraction"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-exact-solve-0012","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"eb06ad11c49f925cab6835888c6d89421d7502daca20c5b67d5b6b99098cfb3e","family_id":"qf-linear-equation-exact-solve","seed":20261039,"semantic_template":"qf-linear-equation-exact-solve/{\"a\":-5,\"b\":0,\"domain\":\"rationals\",\"operation\":\"exact_solve\"}"},"fields":{"title":"Exact Solution of a Linear Equation","stem":"Solve -5x+(0)=0 exactly over the rational numbers; a=-5 is explicitly nonzero.","answer":{"kind":"short_text","value":"0","explanation":"x=−(0)/-5=0; the result is reduced by the gcd to a canonical rational with a positive denominator."},"skills":["rational numbers","canonical fraction"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-exact-solve-0013","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"413489a03aafa9fce1841244a92d4c391ae5fc9f7657400ab4bd82c40a8fa564","family_id":"qf-linear-equation-exact-solve","seed":20261040,"semantic_template":"qf-linear-equation-exact-solve/{\"a\":-4,\"b\":7,\"domain\":\"rationals\",\"operation\":\"exact_solve\"}"},"fields":{"title":"Exact Solution of a Linear Equation","stem":"Solve -4x+(7)=0 exactly over the rational numbers; a=-4 is explicitly nonzero.","answer":{"kind":"short_text","value":"7/4","explanation":"x=−(7)/-4=7/4; the result is reduced by the gcd to a canonical rational with a positive denominator."},"skills":["rational numbers","canonical fraction"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-exact-solve-0014","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a51fb3d2293b1502bf352bac046e53b9aa60548da2c3dc3cfd699d7855ffe8d9","family_id":"qf-linear-equation-exact-solve","seed":20261041,"semantic_template":"qf-linear-equation-exact-solve/{\"a\":-3,\"b\":14,\"domain\":\"rationals\",\"operation\":\"exact_solve\"}"},"fields":{"title":"Exact Solution of a Linear Equation","stem":"Solve -3x+(14)=0 exactly over the rational numbers; a=-3 is explicitly nonzero.","answer":{"kind":"short_text","value":"14/3","explanation":"x=−(14)/-3=14/3; the result is reduced by the gcd to a canonical rational with a positive denominator."},"skills":["rational numbers","canonical fraction"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-exact-solve-0015","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4c5c4c0b3c38387c69c8324d3765fc684c3bc429757328d8a6324487548c9137","family_id":"qf-linear-equation-exact-solve","seed":20261042,"semantic_template":"qf-linear-equation-exact-solve/{\"a\":-2,\"b\":-10,\"domain\":\"rationals\",\"operation\":\"exact_solve\"}"},"fields":{"title":"Exact Solution of a Linear Equation","stem":"Solve -2x+(-10)=0 exactly over the rational numbers; a=-2 is explicitly nonzero.","answer":{"kind":"short_text","value":"-5","explanation":"x=−(-10)/-2=-5; the result is reduced by the gcd to a canonical rational with a positive denominator."},"skills":["rational numbers","canonical fraction"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-exact-solve-0016","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"609bfed76e60c92500e2775b09499ea14de2240d97b682cd81ec759ff93c6a07","family_id":"qf-linear-equation-exact-solve","seed":20261043,"semantic_template":"qf-linear-equation-exact-solve/{\"a\":-1,\"b\":-3,\"domain\":\"rationals\",\"operation\":\"exact_solve\"}"},"fields":{"title":"Exact Solution of a Linear Equation","stem":"Solve -1x+(-3)=0 exactly over the rational numbers; a=-1 is explicitly nonzero.","answer":{"kind":"short_text","value":"-3","explanation":"x=−(-3)/-1=-3; the result is reduced by the gcd to a canonical rational with a positive denominator."},"skills":["rational numbers","canonical fraction"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-exact-solve-0017","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"552e0665efb99936067c3e2169800183468579c598b64810a55b4c33c09b0a64","family_id":"qf-linear-equation-exact-solve","seed":20261044,"semantic_template":"qf-linear-equation-exact-solve/{\"a\":1,\"b\":4,\"domain\":\"rationals\",\"operation\":\"exact_solve\"}"},"fields":{"title":"Exact Solution of a Linear Equation","stem":"Solve 1x+(4)=0 exactly over the rational numbers; a=1 is explicitly nonzero.","answer":{"kind":"short_text","value":"-4","explanation":"x=−(4)/1=-4; the result is reduced by the gcd to a canonical rational with a positive denominator."},"skills":["rational numbers","canonical fraction"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-exact-solve-0018","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1f1ba974398c880a77e6b7573ffb626197661e8e9d0202d76955ca9edc00ef4e","family_id":"qf-linear-equation-exact-solve","seed":20261045,"semantic_template":"qf-linear-equation-exact-solve/{\"a\":1,\"b\":11,\"domain\":\"rationals\",\"operation\":\"exact_solve\"}"},"fields":{"title":"Exact Solution of a Linear Equation","stem":"Solve 1x+(11)=0 exactly over the rational numbers; a=1 is explicitly nonzero.","answer":{"kind":"short_text","value":"-11","explanation":"x=−(11)/1=-11; the result is reduced by the gcd to a canonical rational with a positive denominator."},"skills":["rational numbers","canonical fraction"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-exact-solve-0019","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c329df425c824e80fe00a33f424245b4919ab63e87c803e45c38e981d73c107a","family_id":"qf-linear-equation-exact-solve","seed":20261046,"semantic_template":"qf-linear-equation-exact-solve/{\"a\":2,\"b\":-13,\"domain\":\"rationals\",\"operation\":\"exact_solve\"}"},"fields":{"title":"Exact Solution of a Linear Equation","stem":"Solve 2x+(-13)=0 exactly over the rational numbers; a=2 is explicitly nonzero.","answer":{"kind":"short_text","value":"13/2","explanation":"x=−(-13)/2=13/2; the result is reduced by the gcd to a canonical rational with a positive denominator."},"skills":["rational numbers","canonical fraction"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-exact-solve-0020","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b72c580be7c9c86299f860f0fc54eeb58b86ae1c8ad4d6b67ecb734cb6b55c19","family_id":"qf-linear-equation-exact-solve","seed":20261047,"semantic_template":"qf-linear-equation-exact-solve/{\"a\":3,\"b\":-6,\"domain\":\"rationals\",\"operation\":\"exact_solve\"}"},"fields":{"title":"Exact Solution of a Linear Equation","stem":"Solve 3x+(-6)=0 exactly over the rational numbers; a=3 is explicitly nonzero.","answer":{"kind":"short_text","value":"2","explanation":"x=−(-6)/3=2; the result is reduced by the gcd to a canonical rational with a positive denominator."},"skills":["rational numbers","canonical fraction"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-exact-solve-0021","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"eaaf2097669816e696247b7496b13f0b24005d5db0d67486a729f4bf78d53b73","family_id":"qf-linear-equation-exact-solve","seed":20261048,"semantic_template":"qf-linear-equation-exact-solve/{\"a\":4,\"b\":1,\"domain\":\"rationals\",\"operation\":\"exact_solve\"}"},"fields":{"title":"Exact Solution of a Linear Equation","stem":"Solve 4x+(1)=0 exactly over the rational numbers; a=4 is explicitly nonzero.","answer":{"kind":"short_text","value":"-1/4","explanation":"x=−(1)/4=-1/4; the result is reduced by the gcd to a canonical rational with a positive denominator."},"skills":["rational numbers","canonical fraction"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-exact-solve-0022","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"77e7054c06ad710ae2b861ed0032acf1ba9432d746e353f727f914d24274f77c","family_id":"qf-linear-equation-exact-solve","seed":20261049,"semantic_template":"qf-linear-equation-exact-solve/{\"a\":5,\"b\":8,\"domain\":\"rationals\",\"operation\":\"exact_solve\"}"},"fields":{"title":"Exact Solution of a Linear Equation","stem":"Solve 5x+(8)=0 exactly over the rational numbers; a=5 is explicitly nonzero.","answer":{"kind":"short_text","value":"-8/5","explanation":"x=−(8)/5=-8/5; the result is reduced by the gcd to a canonical rational with a positive denominator."},"skills":["rational numbers","canonical fraction"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-exact-solve-0023","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"91029f0b4393bc4b190d0144055caded0e200d1023a9f6cc1d024e5e232ee729","family_id":"qf-linear-equation-exact-solve","seed":20261050,"semantic_template":"qf-linear-equation-exact-solve/{\"a\":-5,\"b\":15,\"domain\":\"rationals\",\"operation\":\"exact_solve\"}"},"fields":{"title":"Exact Solution of a Linear Equation","stem":"Solve -5x+(15)=0 exactly over the rational numbers; a=-5 is explicitly nonzero.","answer":{"kind":"short_text","value":"3","explanation":"x=−(15)/-5=3; the result is reduced by the gcd to a canonical rational with a positive denominator."},"skills":["rational numbers","canonical fraction"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-exact-solve-0024","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"27bba897e4b05c9405be4bb0efdecb254e1d57cb45208d536950ff37a8013a88","family_id":"qf-linear-equation-exact-solve","seed":20261051,"semantic_template":"qf-linear-equation-exact-solve/{\"a\":-4,\"b\":-9,\"domain\":\"rationals\",\"operation\":\"exact_solve\"}"},"fields":{"title":"Exact Solution of a Linear Equation","stem":"Solve -4x+(-9)=0 exactly over the rational numbers; a=-4 is explicitly nonzero.","answer":{"kind":"short_text","value":"-9/4","explanation":"x=−(-9)/-4=-9/4; the result is reduced by the gcd to a canonical rational with a positive denominator."},"skills":["rational numbers","canonical fraction"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-exact-solve-0025","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ebb712afbf61c7136e8b87eb72ccd1d936dab7dfe50e7b7406511be56cb3b196","family_id":"qf-linear-equation-exact-solve","seed":20261052,"semantic_template":"qf-linear-equation-exact-solve/{\"a\":-3,\"b\":-2,\"domain\":\"rationals\",\"operation\":\"exact_solve\"}"},"fields":{"title":"Exact Solution of a Linear Equation","stem":"Solve -3x+(-2)=0 exactly over the rational numbers; a=-3 is explicitly nonzero.","answer":{"kind":"short_text","value":"-2/3","explanation":"x=−(-2)/-3=-2/3; the result is reduced by the gcd to a canonical rational with a positive denominator."},"skills":["rational numbers","canonical fraction"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-solution-verification-0001","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"efdce7dd45caf29b5ee862159044605dbefe9569b3add1133d91ff7a65c7f030","family_id":"qf-linear-equation-solution-verification","seed":20261128,"semantic_template":"qf-linear-equation-solution-verification/{\"a\":-4,\"b\":-14,\"domain\":\"rationals\",\"operation\":\"cross_multiplication_substitution\",\"p\":-7,\"q\":2}"},"fields":{"title":"Cross-Multiplication Check of a Rational Solution","stem":"Over the rational numbers, consider -4x+(-14)=0 and the candidate x=-7/2. Is the candidate a solution?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"q=2≠0 and -4×-7+(-14)×2=0, so the candidate is a solution."},"skills":["rational substitution","cross multiplication"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-solution-verification-0002","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6ad4f56ebff658eeb061bc7a00100d451ea011349abce616e09f16c1413c14e8","family_id":"qf-linear-equation-solution-verification","seed":20261129,"semantic_template":"qf-linear-equation-solution-verification/{\"a\":-3,\"b\":-9,\"domain\":\"rationals\",\"operation\":\"cross_multiplication_substitution\",\"p\":-2,\"q\":1}"},"fields":{"title":"Cross-Multiplication Check of a Rational Solution","stem":"Over the rational numbers, consider -3x+(-9)=0 and the candidate x=-2/1. Is the candidate a solution?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"q=1≠0 and -3×-2+(-9)×1=-3, so the candidate is not a solution."},"skills":["rational substitution","cross multiplication"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-solution-verification-0003","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6270b5fc01006621f261052e73de8af78af2c10a381aa2753e6b281b88cac6d6","family_id":"qf-linear-equation-solution-verification","seed":20261130,"semantic_template":"qf-linear-equation-solution-verification/{\"a\":-2,\"b\":-4,\"domain\":\"rationals\",\"operation\":\"cross_multiplication_substitution\",\"p\":-2,\"q\":1}"},"fields":{"title":"Cross-Multiplication Check of a Rational Solution","stem":"Over the rational numbers, consider -2x+(-4)=0 and the candidate x=-2/1. Is the candidate a solution?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"q=1≠0 and -2×-2+(-4)×1=0, so the candidate is a solution."},"skills":["rational substitution","cross multiplication"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-solution-verification-0004","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7aa392cf669e111ed2bf6d835d428cd917b0d6837c7526c7fe4cd0d3d73b5027","family_id":"qf-linear-equation-solution-verification","seed":20261131,"semantic_template":"qf-linear-equation-solution-verification/{\"a\":-1,\"b\":1,\"domain\":\"rationals\",\"operation\":\"cross_multiplication_substitution\",\"p\":2,\"q\":1}"},"fields":{"title":"Cross-Multiplication Check of a Rational Solution","stem":"Over the rational numbers, consider -1x+(1)=0 and the candidate x=2/1. Is the candidate a solution?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"q=1≠0 and -1×2+(1)×1=-1, so the candidate is not a solution."},"skills":["rational substitution","cross multiplication"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-solution-verification-0005","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"40a9cd28e72d6855802ca77715b2fb2b94914e53c826d12437d4c154c6113257","family_id":"qf-linear-equation-solution-verification","seed":20261132,"semantic_template":"qf-linear-equation-solution-verification/{\"a\":2,\"b\":6,\"domain\":\"rationals\",\"operation\":\"cross_multiplication_substitution\",\"p\":-3,\"q\":1}"},"fields":{"title":"Cross-Multiplication Check of a Rational Solution","stem":"Over the rational numbers, consider 2x+(6)=0 and the candidate x=-3/1. Is the candidate a solution?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"q=1≠0 and 2×-3+(6)×1=0, so the candidate is a solution."},"skills":["rational substitution","cross multiplication"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-solution-verification-0006","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6b5fcc94f131126e168c995b459bb9e06985e77e47faf29d4d1aee884230f8bd","family_id":"qf-linear-equation-solution-verification","seed":20261133,"semantic_template":"qf-linear-equation-solution-verification/{\"a\":1,\"b\":11,\"domain\":\"rationals\",\"operation\":\"cross_multiplication_substitution\",\"p\":-10,\"q\":1}"},"fields":{"title":"Cross-Multiplication Check of a Rational Solution","stem":"Over the rational numbers, consider 1x+(11)=0 and the candidate x=-10/1. Is the candidate a solution?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"q=1≠0 and 1×-10+(11)×1=1, so the candidate is not a solution."},"skills":["rational substitution","cross multiplication"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-solution-verification-0007","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9f85a6c8d261749b2239d69c9e4bba3744d241c01dc2e5907d6694043beefd73","family_id":"qf-linear-equation-solution-verification","seed":20261134,"semantic_template":"qf-linear-equation-solution-verification/{\"a\":2,\"b\":-13,\"domain\":\"rationals\",\"operation\":\"cross_multiplication_substitution\",\"p\":13,\"q\":2}"},"fields":{"title":"Cross-Multiplication Check of a Rational Solution","stem":"Over the rational numbers, consider 2x+(-13)=0 and the candidate x=13/2. Is the candidate a solution?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"q=2≠0 and 2×13+(-13)×2=0, so the candidate is a solution."},"skills":["rational substitution","cross multiplication"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-solution-verification-0008","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ae15be4595dd0357537251a2199df47db3c8245296a3f2e4628989f9b9010e40","family_id":"qf-linear-equation-solution-verification","seed":20261135,"semantic_template":"qf-linear-equation-solution-verification/{\"a\":3,\"b\":-8,\"domain\":\"rationals\",\"operation\":\"cross_multiplication_substitution\",\"p\":3,\"q\":1}"},"fields":{"title":"Cross-Multiplication Check of a Rational Solution","stem":"Over the rational numbers, consider 3x+(-8)=0 and the candidate x=3/1. Is the candidate a solution?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"q=1≠0 and 3×3+(-8)×1=1, so the candidate is not a solution."},"skills":["rational substitution","cross multiplication"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-solution-verification-0009","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"43f0151cc47cae53e6c8285490bfd974159d9a298bf7654a52feeb350af0b536","family_id":"qf-linear-equation-solution-verification","seed":20261136,"semantic_template":"qf-linear-equation-solution-verification/{\"a\":4,\"b\":-3,\"domain\":\"rationals\",\"operation\":\"cross_multiplication_substitution\",\"p\":3,\"q\":4}"},"fields":{"title":"Cross-Multiplication Check of a Rational Solution","stem":"Over the rational numbers, consider 4x+(-3)=0 and the candidate x=3/4. Is the candidate a solution?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"q=4≠0 and 4×3+(-3)×4=0, so the candidate is a solution."},"skills":["rational substitution","cross multiplication"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-solution-verification-0010","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"509fc03c98cbdb07496cc46d6fffbda61c8393339dbc08fa4eee47a96ff6c1d5","family_id":"qf-linear-equation-solution-verification","seed":20261137,"semantic_template":"qf-linear-equation-solution-verification/{\"a\":-4,\"b\":2,\"domain\":\"rationals\",\"operation\":\"cross_multiplication_substitution\",\"p\":1,\"q\":1}"},"fields":{"title":"Cross-Multiplication Check of a Rational Solution","stem":"Over the rational numbers, consider -4x+(2)=0 and the candidate x=1/1. Is the candidate a solution?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"q=1≠0 and -4×1+(2)×1=-2, so the candidate is not a solution."},"skills":["rational substitution","cross multiplication"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-solution-verification-0011","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a7a75505b52bbba8b00df4867dab7082dcc92eead25ccdca43df76da0b20d799","family_id":"qf-linear-equation-solution-verification","seed":20261138,"semantic_template":"qf-linear-equation-solution-verification/{\"a\":-3,\"b\":7,\"domain\":\"rationals\",\"operation\":\"cross_multiplication_substitution\",\"p\":7,\"q\":3}"},"fields":{"title":"Cross-Multiplication Check of a Rational Solution","stem":"Over the rational numbers, consider -3x+(7)=0 and the candidate x=7/3. Is the candidate a solution?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"q=3≠0 and -3×7+(7)×3=0, so the candidate is a solution."},"skills":["rational substitution","cross multiplication"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-solution-verification-0012","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6f28b843278dbf90291d8a0405b39d55219516f9164e9192ba6b9a736f884d75","family_id":"qf-linear-equation-solution-verification","seed":20261139,"semantic_template":"qf-linear-equation-solution-verification/{\"a\":-2,\"b\":12,\"domain\":\"rationals\",\"operation\":\"cross_multiplication_substitution\",\"p\":7,\"q\":1}"},"fields":{"title":"Cross-Multiplication Check of a Rational Solution","stem":"Over the rational numbers, consider -2x+(12)=0 and the candidate x=7/1. Is the candidate a solution?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"q=1≠0 and -2×7+(12)×1=-2, so the candidate is not a solution."},"skills":["rational substitution","cross multiplication"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-solution-verification-0013","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9b25015b15d7be76a6bf0699d4ce3299ab65614df707c48b73bd9c7c005655c1","family_id":"qf-linear-equation-solution-verification","seed":20261140,"semantic_template":"qf-linear-equation-solution-verification/{\"a\":-1,\"b\":-12,\"domain\":\"rationals\",\"operation\":\"cross_multiplication_substitution\",\"p\":-12,\"q\":1}"},"fields":{"title":"Cross-Multiplication Check of a Rational Solution","stem":"Over the rational numbers, consider -1x+(-12)=0 and the candidate x=-12/1. Is the candidate a solution?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"q=1≠0 and -1×-12+(-12)×1=0, so the candidate is a solution."},"skills":["rational substitution","cross multiplication"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-solution-verification-0014","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e6d33720e4b654c497c616c8022dcde08b68d0768fb2b3fce6dc767830dd7ae7","family_id":"qf-linear-equation-solution-verification","seed":20261141,"semantic_template":"qf-linear-equation-solution-verification/{\"a\":2,\"b\":-7,\"domain\":\"rationals\",\"operation\":\"cross_multiplication_substitution\",\"p\":4,\"q\":1}"},"fields":{"title":"Cross-Multiplication Check of a Rational Solution","stem":"Over the rational numbers, consider 2x+(-7)=0 and the candidate x=4/1. Is the candidate a solution?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"q=1≠0 and 2×4+(-7)×1=1, so the candidate is not a solution."},"skills":["rational substitution","cross multiplication"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-solution-verification-0015","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c83761d97bf61f1cbf1d95aa4f8971a42370f409fe4afb52576dc1a242c09de7","family_id":"qf-linear-equation-solution-verification","seed":20261142,"semantic_template":"qf-linear-equation-solution-verification/{\"a\":1,\"b\":-2,\"domain\":\"rationals\",\"operation\":\"cross_multiplication_substitution\",\"p\":2,\"q\":1}"},"fields":{"title":"Cross-Multiplication Check of a Rational Solution","stem":"Over the rational numbers, consider 1x+(-2)=0 and the candidate x=2/1. Is the candidate a solution?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"q=1≠0 and 1×2+(-2)×1=0, so the candidate is a solution."},"skills":["rational substitution","cross multiplication"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-solution-verification-0016","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d4a410278b9a32a7777e18d369bbc337cd5f6f93aa7274a24343a44e051b16c2","family_id":"qf-linear-equation-solution-verification","seed":20261143,"semantic_template":"qf-linear-equation-solution-verification/{\"a\":2,\"b\":3,\"domain\":\"rationals\",\"operation\":\"cross_multiplication_substitution\",\"p\":-1,\"q\":1}"},"fields":{"title":"Cross-Multiplication Check of a Rational Solution","stem":"Over the rational numbers, consider 2x+(3)=0 and the candidate x=-1/1. Is the candidate a solution?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"q=1≠0 and 2×-1+(3)×1=1, so the candidate is not a solution."},"skills":["rational substitution","cross multiplication"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-solution-verification-0017","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7c657a6ff29724aa470f7cd366d119a0fa7ebfdb2fae3f4aaa4e33bcc9de1a15","family_id":"qf-linear-equation-solution-verification","seed":20261144,"semantic_template":"qf-linear-equation-solution-verification/{\"a\":3,\"b\":8,\"domain\":\"rationals\",\"operation\":\"cross_multiplication_substitution\",\"p\":-8,\"q\":3}"},"fields":{"title":"Cross-Multiplication Check of a Rational Solution","stem":"Over the rational numbers, consider 3x+(8)=0 and the candidate x=-8/3. Is the candidate a solution?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"q=3≠0 and 3×-8+(8)×3=0, so the candidate is a solution."},"skills":["rational substitution","cross multiplication"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-solution-verification-0018","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7fa7274290ead16a261ffa182c658e4ec738d0465b1181153280187ffe711057","family_id":"qf-linear-equation-solution-verification","seed":20261145,"semantic_template":"qf-linear-equation-solution-verification/{\"a\":4,\"b\":13,\"domain\":\"rationals\",\"operation\":\"cross_multiplication_substitution\",\"p\":-3,\"q\":1}"},"fields":{"title":"Cross-Multiplication Check of a Rational Solution","stem":"Over the rational numbers, consider 4x+(13)=0 and the candidate x=-3/1. Is the candidate a solution?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"q=1≠0 and 4×-3+(13)×1=1, so the candidate is not a solution."},"skills":["rational substitution","cross multiplication"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-solution-verification-0019","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6e11aa68f383eb5985cfe991d3200824477a3806a5e33f8c0ac2681bd811bc9c","family_id":"qf-linear-equation-solution-verification","seed":20261146,"semantic_template":"qf-linear-equation-solution-verification/{\"a\":-4,\"b\":-11,\"domain\":\"rationals\",\"operation\":\"cross_multiplication_substitution\",\"p\":-11,\"q\":4}"},"fields":{"title":"Cross-Multiplication Check of a Rational Solution","stem":"Over the rational numbers, consider -4x+(-11)=0 and the candidate x=-11/4. Is the candidate a solution?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"q=4≠0 and -4×-11+(-11)×4=0, so the candidate is a solution."},"skills":["rational substitution","cross multiplication"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-solution-verification-0020","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"92267cbf8a2fd5e8be0da94abae609f085df45c64d14c946c8dca4aa91e557c2","family_id":"qf-linear-equation-solution-verification","seed":20261147,"semantic_template":"qf-linear-equation-solution-verification/{\"a\":-3,\"b\":-6,\"domain\":\"rationals\",\"operation\":\"cross_multiplication_substitution\",\"p\":-1,\"q\":1}"},"fields":{"title":"Cross-Multiplication Check of a Rational Solution","stem":"Over the rational numbers, consider -3x+(-6)=0 and the candidate x=-1/1. Is the candidate a solution?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"q=1≠0 and -3×-1+(-6)×1=-3, so the candidate is not a solution."},"skills":["rational substitution","cross multiplication"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-solution-verification-0021","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f8df356f905b5600ab89a5d288ab694af7509a75bcb090ad6720b9a471b57204","family_id":"qf-linear-equation-solution-verification","seed":20261148,"semantic_template":"qf-linear-equation-solution-verification/{\"a\":-2,\"b\":-1,\"domain\":\"rationals\",\"operation\":\"cross_multiplication_substitution\",\"p\":-1,\"q\":2}"},"fields":{"title":"Cross-Multiplication Check of a Rational Solution","stem":"Over the rational numbers, consider -2x+(-1)=0 and the candidate x=-1/2. Is the candidate a solution?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"q=2≠0 and -2×-1+(-1)×2=0, so the candidate is a solution."},"skills":["rational substitution","cross multiplication"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-solution-verification-0022","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"337cd0d3aa3884a32f1b3f7e7de2a6dfd913eae43ea43743c3d7778729ea5c53","family_id":"qf-linear-equation-solution-verification","seed":20261149,"semantic_template":"qf-linear-equation-solution-verification/{\"a\":-1,\"b\":4,\"domain\":\"rationals\",\"operation\":\"cross_multiplication_substitution\",\"p\":5,\"q\":1}"},"fields":{"title":"Cross-Multiplication Check of a Rational Solution","stem":"Over the rational numbers, consider -1x+(4)=0 and the candidate x=5/1. Is the candidate a solution?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"q=1≠0 and -1×5+(4)×1=-1, so the candidate is not a solution."},"skills":["rational substitution","cross multiplication"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-solution-verification-0023","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3fef8cd4cb824d0b3d20310d8db24f2987db32141cb26ada093e48a935f65db2","family_id":"qf-linear-equation-solution-verification","seed":20261150,"semantic_template":"qf-linear-equation-solution-verification/{\"a\":2,\"b\":9,\"domain\":\"rationals\",\"operation\":\"cross_multiplication_substitution\",\"p\":-9,\"q\":2}"},"fields":{"title":"Cross-Multiplication Check of a Rational Solution","stem":"Over the rational numbers, consider 2x+(9)=0 and the candidate x=-9/2. Is the candidate a solution?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"q=2≠0 and 2×-9+(9)×2=0, so the candidate is a solution."},"skills":["rational substitution","cross multiplication"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-solution-verification-0024","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5cc5740b6571806cf27751b8f821316dc8e13c7f47023b5e31acfa543d229fa1","family_id":"qf-linear-equation-solution-verification","seed":20261151,"semantic_template":"qf-linear-equation-solution-verification/{\"a\":1,\"b\":14,\"domain\":\"rationals\",\"operation\":\"cross_multiplication_substitution\",\"p\":-13,\"q\":1}"},"fields":{"title":"Cross-Multiplication Check of a Rational Solution","stem":"Over the rational numbers, consider 1x+(14)=0 and the candidate x=-13/1. Is the candidate a solution?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"q=1≠0 and 1×-13+(14)×1=1, so the candidate is not a solution."},"skills":["rational substitution","cross multiplication"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-solution-verification-0025","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d5cbc50b59932ff143aadbde5d9968fa605dd6bbb986dde0f2755b9bbfbfeb4e","family_id":"qf-linear-equation-solution-verification","seed":20261152,"semantic_template":"qf-linear-equation-solution-verification/{\"a\":2,\"b\":-10,\"domain\":\"rationals\",\"operation\":\"cross_multiplication_substitution\",\"p\":5,\"q\":1}"},"fields":{"title":"Cross-Multiplication Check of a Rational Solution","stem":"Over the rational numbers, consider 2x+(-10)=0 and the candidate x=5/1. Is the candidate a solution?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"q=1≠0 and 2×5+(-10)×1=0, so the candidate is a solution."},"skills":["rational substitution","cross multiplication"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-solution-class-0001","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3cfabfab0ad9ea0cda673f64cd3ad4b47b00cdf8be7929a33188afdad475f45d","family_id":"qf-linear-equation-solution-class","seed":20261228,"semantic_template":"qf-linear-equation-solution-class/{\"a\":0,\"b\":0,\"domain\":\"rationals\",\"operation\":\"solution_class\"}"},"fields":{"title":"Solution Classification of a Linear Equation","stem":"Over the rational numbers, classify the solution set of 0x+(0)=0.","answer":{"kind":"short_text","value":"all rational numbers are solutions","explanation":"With a=0 and b=0, the equation is 0=0, so every rational number is a solution."},"skills":["solution classification","degenerate constant equality"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-solution-class-0002","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"08bed2dab53dfc1fc260964f28619dcf27f417ee09a9048645a1ed845f8f200d","family_id":"qf-linear-equation-solution-class","seed":20261229,"semantic_template":"qf-linear-equation-solution-class/{\"a\":0,\"b\":1,\"domain\":\"rationals\",\"operation\":\"solution_class\"}"},"fields":{"title":"Solution Classification of a Linear Equation","stem":"Over the rational numbers, classify the solution set of 0x+(1)=0.","answer":{"kind":"short_text","value":"no solution","explanation":"With a=0 and b=1≠0, the equation is 1=0, so it has no solution."},"skills":["solution classification","degenerate constant equality"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-solution-class-0003","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"65e5212dfd2d3165ffa7f5c03be432c60c14347e3fad63c40a1d6c971fe53c16","family_id":"qf-linear-equation-solution-class","seed":20261230,"semantic_template":"qf-linear-equation-solution-class/{\"a\":0,\"b\":2,\"domain\":\"rationals\",\"operation\":\"solution_class\"}"},"fields":{"title":"Solution Classification of a Linear Equation","stem":"Over the rational numbers, classify the solution set of 0x+(2)=0.","answer":{"kind":"short_text","value":"no solution","explanation":"With a=0 and b=2≠0, the equation is 2=0, so it has no solution."},"skills":["solution classification","degenerate constant equality"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-solution-class-0004","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ce17978f25978a3aad5d30e2bfd516498cb8f8b2ff16d3ccd2c695b4773aa680","family_id":"qf-linear-equation-solution-class","seed":20261231,"semantic_template":"qf-linear-equation-solution-class/{\"a\":0,\"b\":3,\"domain\":\"rationals\",\"operation\":\"solution_class\"}"},"fields":{"title":"Solution Classification of a Linear Equation","stem":"Over the rational numbers, classify the solution set of 0x+(3)=0.","answer":{"kind":"short_text","value":"no solution","explanation":"With a=0 and b=3≠0, the equation is 3=0, so it has no solution."},"skills":["solution classification","degenerate constant equality"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-solution-class-0005","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a775797fcfa40b4f59eb7a7c4f6e74318142d011decb3ff3395118db240da9c6","family_id":"qf-linear-equation-solution-class","seed":20261232,"semantic_template":"qf-linear-equation-solution-class/{\"a\":0,\"b\":4,\"domain\":\"rationals\",\"operation\":\"solution_class\"}"},"fields":{"title":"Solution Classification of a Linear Equation","stem":"Over the rational numbers, classify the solution set of 0x+(4)=0.","answer":{"kind":"short_text","value":"no solution","explanation":"With a=0 and b=4≠0, the equation is 4=0, so it has no solution."},"skills":["solution classification","degenerate constant equality"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-solution-class-0006","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"52ddc20b0a16ddb1fd3f595e3d48ebfb8eb856b45fc7613b7c6d76dc51e859f6","family_id":"qf-linear-equation-solution-class","seed":20261233,"semantic_template":"qf-linear-equation-solution-class/{\"a\":0,\"b\":5,\"domain\":\"rationals\",\"operation\":\"solution_class\"}"},"fields":{"title":"Solution Classification of a Linear Equation","stem":"Over the rational numbers, classify the solution set of 0x+(5)=0.","answer":{"kind":"short_text","value":"no solution","explanation":"With a=0 and b=5≠0, the equation is 5=0, so it has no solution."},"skills":["solution classification","degenerate constant equality"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-solution-class-0007","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"bffaeff8819a4cb81fe8d1fbb850b2677cfcc543d4ce6f8edba5424a19231a7f","family_id":"qf-linear-equation-solution-class","seed":20261234,"semantic_template":"qf-linear-equation-solution-class/{\"a\":0,\"b\":6,\"domain\":\"rationals\",\"operation\":\"solution_class\"}"},"fields":{"title":"Solution Classification of a Linear Equation","stem":"Over the rational numbers, classify the solution set of 0x+(6)=0.","answer":{"kind":"short_text","value":"no solution","explanation":"With a=0 and b=6≠0, the equation is 6=0, so it has no solution."},"skills":["solution classification","degenerate constant equality"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-solution-class-0008","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1a9f35ae455bb4c91d1cb1064d39784445e82097b4e34951e9acf4e3efe14b75","family_id":"qf-linear-equation-solution-class","seed":20261235,"semantic_template":"qf-linear-equation-solution-class/{\"a\":0,\"b\":7,\"domain\":\"rationals\",\"operation\":\"solution_class\"}"},"fields":{"title":"Solution Classification of a Linear Equation","stem":"Over the rational numbers, classify the solution set of 0x+(7)=0.","answer":{"kind":"short_text","value":"no solution","explanation":"With a=0 and b=7≠0, the equation is 7=0, so it has no solution."},"skills":["solution classification","degenerate constant equality"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-solution-class-0009","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ac32561a115913ec6af8f01bef20db80a19bc70f6f8fa48db263977a9f4085a1","family_id":"qf-linear-equation-solution-class","seed":20261236,"semantic_template":"qf-linear-equation-solution-class/{\"a\":0,\"b\":8,\"domain\":\"rationals\",\"operation\":\"solution_class\"}"},"fields":{"title":"Solution Classification of a Linear Equation","stem":"Over the rational numbers, classify the solution set of 0x+(8)=0.","answer":{"kind":"short_text","value":"no solution","explanation":"With a=0 and b=8≠0, the equation is 8=0, so it has no solution."},"skills":["solution classification","degenerate constant equality"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-solution-class-0010","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a5f1062527e7dfe76585c8e59702d4970b3b736c69ab5b6973abd178c2f4c619","family_id":"qf-linear-equation-solution-class","seed":20261237,"semantic_template":"qf-linear-equation-solution-class/{\"a\":3,\"b\":-3,\"domain\":\"rationals\",\"operation\":\"solution_class\"}"},"fields":{"title":"Solution Classification of a Linear Equation","stem":"Over the rational numbers, classify the solution set of 3x+(-3)=0.","answer":{"kind":"short_text","value":"unique solution x=1","explanation":"Because a=3≠0, the equation has the unique solution x=1."},"skills":["solution classification","degenerate constant equality"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-solution-class-0011","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"48709500d018abaa1d2f0d5666bfe91825549b648411d400a81a5657540a95c6","family_id":"qf-linear-equation-solution-class","seed":20261238,"semantic_template":"qf-linear-equation-solution-class/{\"a\":4,\"b\":-2,\"domain\":\"rationals\",\"operation\":\"solution_class\"}"},"fields":{"title":"Solution Classification of a Linear Equation","stem":"Over the rational numbers, classify the solution set of 4x+(-2)=0.","answer":{"kind":"short_text","value":"unique solution x=1/2","explanation":"Because a=4≠0, the equation has the unique solution x=1/2."},"skills":["solution classification","degenerate constant equality"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-solution-class-0012","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4a31afee6d48472c44c742c5965cbcffbc167a60a2c7ea9d328e65b3c9bf1a3e","family_id":"qf-linear-equation-solution-class","seed":20261239,"semantic_template":"qf-linear-equation-solution-class/{\"a\":5,\"b\":-1,\"domain\":\"rationals\",\"operation\":\"solution_class\"}"},"fields":{"title":"Solution Classification of a Linear Equation","stem":"Over the rational numbers, classify the solution set of 5x+(-1)=0.","answer":{"kind":"short_text","value":"unique solution x=1/5","explanation":"Because a=5≠0, the equation has the unique solution x=1/5."},"skills":["solution classification","degenerate constant equality"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-solution-class-0013","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"243d3086b05b96de895796784e6c3a438267593835b1f2c853cf940ddbda4a66","family_id":"qf-linear-equation-solution-class","seed":20261240,"semantic_template":"qf-linear-equation-solution-class/{\"a\":6,\"b\":0,\"domain\":\"rationals\",\"operation\":\"solution_class\"}"},"fields":{"title":"Solution Classification of a Linear Equation","stem":"Over the rational numbers, classify the solution set of 6x+(0)=0.","answer":{"kind":"short_text","value":"unique solution x=0","explanation":"Because a=6≠0, the equation has the unique solution x=0."},"skills":["solution classification","degenerate constant equality"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-solution-class-0014","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ad8b947fc2e31bac309104169b6ff7c9dbd27c3f3dfc7f48ffccbe3f46abed15","family_id":"qf-linear-equation-solution-class","seed":20261241,"semantic_template":"qf-linear-equation-solution-class/{\"a\":7,\"b\":1,\"domain\":\"rationals\",\"operation\":\"solution_class\"}"},"fields":{"title":"Solution Classification of a Linear Equation","stem":"Over the rational numbers, classify the solution set of 7x+(1)=0.","answer":{"kind":"short_text","value":"unique solution x=-1/7","explanation":"Because a=7≠0, the equation has the unique solution x=-1/7."},"skills":["solution classification","degenerate constant equality"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-solution-class-0015","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"88e7073a051c12706ff5cfcabc3b51f79bba902ce8c6db7673aef12cee0b92e1","family_id":"qf-linear-equation-solution-class","seed":20261242,"semantic_template":"qf-linear-equation-solution-class/{\"a\":1,\"b\":2,\"domain\":\"rationals\",\"operation\":\"solution_class\"}"},"fields":{"title":"Solution Classification of a Linear Equation","stem":"Over the rational numbers, classify the solution set of 1x+(2)=0.","answer":{"kind":"short_text","value":"unique solution x=-2","explanation":"Because a=1≠0, the equation has the unique solution x=-2."},"skills":["solution classification","degenerate constant equality"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-solution-class-0016","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6dba6030b10377067a1d5c3770c03034c5db81c745c1f96b0bbe4e1869ca4811","family_id":"qf-linear-equation-solution-class","seed":20261243,"semantic_template":"qf-linear-equation-solution-class/{\"a\":2,\"b\":3,\"domain\":\"rationals\",\"operation\":\"solution_class\"}"},"fields":{"title":"Solution Classification of a Linear Equation","stem":"Over the rational numbers, classify the solution set of 2x+(3)=0.","answer":{"kind":"short_text","value":"unique solution x=-3/2","explanation":"Because a=2≠0, the equation has the unique solution x=-3/2."},"skills":["solution classification","degenerate constant equality"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-solution-class-0017","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"cc8770ffeff3b906f908468262276480eb2cf62c64d2ad0cbe46d6ad05c2ffc6","family_id":"qf-linear-equation-solution-class","seed":20261244,"semantic_template":"qf-linear-equation-solution-class/{\"a\":3,\"b\":4,\"domain\":\"rationals\",\"operation\":\"solution_class\"}"},"fields":{"title":"Solution Classification of a Linear Equation","stem":"Over the rational numbers, classify the solution set of 3x+(4)=0.","answer":{"kind":"short_text","value":"unique solution x=-4/3","explanation":"Because a=3≠0, the equation has the unique solution x=-4/3."},"skills":["solution classification","degenerate constant equality"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-solution-class-0018","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1473702e4d732e64642dfe1f8928eb5abf838eaf546eabed629c921c6b826655","family_id":"qf-linear-equation-solution-class","seed":20261245,"semantic_template":"qf-linear-equation-solution-class/{\"a\":4,\"b\":5,\"domain\":\"rationals\",\"operation\":\"solution_class\"}"},"fields":{"title":"Solution Classification of a Linear Equation","stem":"Over the rational numbers, classify the solution set of 4x+(5)=0.","answer":{"kind":"short_text","value":"unique solution x=-5/4","explanation":"Because a=4≠0, the equation has the unique solution x=-5/4."},"skills":["solution classification","degenerate constant equality"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-solution-class-0019","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2a9ab2047bfa8f4a848e0c29bf1e474b55921cef6e352fdcd254ddd45c8196b1","family_id":"qf-linear-equation-solution-class","seed":20261246,"semantic_template":"qf-linear-equation-solution-class/{\"a\":5,\"b\":6,\"domain\":\"rationals\",\"operation\":\"solution_class\"}"},"fields":{"title":"Solution Classification of a Linear Equation","stem":"Over the rational numbers, classify the solution set of 5x+(6)=0.","answer":{"kind":"short_text","value":"unique solution x=-6/5","explanation":"Because a=5≠0, the equation has the unique solution x=-6/5."},"skills":["solution classification","degenerate constant equality"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-solution-class-0020","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1e5da7f26b4bf46f117bbd77f91eda168a35353216b6abefd00532779e9fca31","family_id":"qf-linear-equation-solution-class","seed":20261247,"semantic_template":"qf-linear-equation-solution-class/{\"a\":6,\"b\":7,\"domain\":\"rationals\",\"operation\":\"solution_class\"}"},"fields":{"title":"Solution Classification of a Linear Equation","stem":"Over the rational numbers, classify the solution set of 6x+(7)=0.","answer":{"kind":"short_text","value":"unique solution x=-7/6","explanation":"Because a=6≠0, the equation has the unique solution x=-7/6."},"skills":["solution classification","degenerate constant equality"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-solution-class-0021","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ebba65e3db747eb5fe8b73ad3cd6bb99660af1d476c519e6dd6cefdc087a7f92","family_id":"qf-linear-equation-solution-class","seed":20261248,"semantic_template":"qf-linear-equation-solution-class/{\"a\":7,\"b\":8,\"domain\":\"rationals\",\"operation\":\"solution_class\"}"},"fields":{"title":"Solution Classification of a Linear Equation","stem":"Over the rational numbers, classify the solution set of 7x+(8)=0.","answer":{"kind":"short_text","value":"unique solution x=-8/7","explanation":"Because a=7≠0, the equation has the unique solution x=-8/7."},"skills":["solution classification","degenerate constant equality"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-solution-class-0022","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b948ef7abc1032f7b1b9b3dd31c55570b8fb392076df82e1617ae5018bf44685","family_id":"qf-linear-equation-solution-class","seed":20261249,"semantic_template":"qf-linear-equation-solution-class/{\"a\":1,\"b\":9,\"domain\":\"rationals\",\"operation\":\"solution_class\"}"},"fields":{"title":"Solution Classification of a Linear Equation","stem":"Over the rational numbers, classify the solution set of 1x+(9)=0.","answer":{"kind":"short_text","value":"unique solution x=-9","explanation":"Because a=1≠0, the equation has the unique solution x=-9."},"skills":["solution classification","degenerate constant equality"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-solution-class-0023","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"274cb6a00dcfc6f260360ea7b26608f17d6e9fe2b8922c718603a1b6a1ca6bb8","family_id":"qf-linear-equation-solution-class","seed":20261250,"semantic_template":"qf-linear-equation-solution-class/{\"a\":2,\"b\":10,\"domain\":\"rationals\",\"operation\":\"solution_class\"}"},"fields":{"title":"Solution Classification of a Linear Equation","stem":"Over the rational numbers, classify the solution set of 2x+(10)=0.","answer":{"kind":"short_text","value":"unique solution x=-5","explanation":"Because a=2≠0, the equation has the unique solution x=-5."},"skills":["solution classification","degenerate constant equality"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-solution-class-0024","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"72bb1a92078f78f5703995b2170a4707de6544ebaaab11a0b39acabdd29e4168","family_id":"qf-linear-equation-solution-class","seed":20261251,"semantic_template":"qf-linear-equation-solution-class/{\"a\":3,\"b\":11,\"domain\":\"rationals\",\"operation\":\"solution_class\"}"},"fields":{"title":"Solution Classification of a Linear Equation","stem":"Over the rational numbers, classify the solution set of 3x+(11)=0.","answer":{"kind":"short_text","value":"unique solution x=-11/3","explanation":"Because a=3≠0, the equation has the unique solution x=-11/3."},"skills":["solution classification","degenerate constant equality"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260927-linear-equation-solution-class-0025","batch_id":"batch-20260927-linear-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c859c8ac269a9a422f27b9afdeae325b05a15c07e58cf3d679ce95937244ec5d","family_id":"qf-linear-equation-solution-class","seed":20261252,"semantic_template":"qf-linear-equation-solution-class/{\"a\":4,\"b\":12,\"domain\":\"rationals\",\"operation\":\"solution_class\"}"},"fields":{"title":"Solution Classification of a Linear Equation","stem":"Over the rational numbers, classify the solution set of 4x+(12)=0.","answer":{"kind":"short_text","value":"unique solution x=-3","explanation":"Because a=4≠0, the equation has the unique solution x=-3."},"skills":["solution classification","degenerate constant equality"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}