{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260924-equation-solution-verification-0001","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2a93cb15d7d53f57958c7c08daa4f20c9d03aef3ab16530d92144529ce648f06","family_id":"qf-equation-solution-verification","seed":20260925,"semantic_template":"qf-equation-solution-verification/{\"a\":-12,\"b\":-8,\"candidate\":5,\"domain\":\"integers\",\"form\":\"x+a=b\"}"},"fields":{"title":"Checking a Candidate Solution by Substitution","stem":"Over the integers, consider x+(-12)=-8 with candidate x=5. After substitution into the original equation, is the candidate a solution?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"The left side is 5+(-12)=-7, while the right side is -8; the two sides are not equal."},"skills":["verification by substitution","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-20260924-equation-solution-verification-0002","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c3a15d38171d32852f7bbf9967bf06d3324e67a2b369d9122e240617f2a6bc05","family_id":"qf-equation-solution-verification","seed":20260926,"semantic_template":"qf-equation-solution-verification/{\"a\":-11,\"b\":-7,\"candidate\":4,\"domain\":\"integers\",\"form\":\"x+a=b\"}"},"fields":{"title":"Checking a Candidate Solution by Substitution","stem":"Over the integers, consider x+(-11)=-7 with candidate x=4. After substitution into the original equation, is the candidate a solution?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"The left side is 4+(-11)=-7, while the right side is -7; the two sides are equal."},"skills":["verification by substitution","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-20260924-equation-solution-verification-0003","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e714d4c9e62edaeddb24b488c89410e15bf42490b40a483c0afa7083d4b8d772","family_id":"qf-equation-solution-verification","seed":20260927,"semantic_template":"qf-equation-solution-verification/{\"a\":-10,\"b\":-6,\"candidate\":5,\"domain\":\"integers\",\"form\":\"x+a=b\"}"},"fields":{"title":"Checking a Candidate Solution by Substitution","stem":"Over the integers, consider x+(-10)=-6 with candidate x=5. After substitution into the original equation, is the candidate a solution?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"The left side is 5+(-10)=-5, while the right side is -6; the two sides are not equal."},"skills":["verification by substitution","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-20260924-equation-solution-verification-0004","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9a53eeebb32c33b62329149ca199535596a4daaba3d6efed664efd17bf7f5527","family_id":"qf-equation-solution-verification","seed":20260928,"semantic_template":"qf-equation-solution-verification/{\"a\":-9,\"b\":-5,\"candidate\":4,\"domain\":\"integers\",\"form\":\"x+a=b\"}"},"fields":{"title":"Checking a Candidate Solution by Substitution","stem":"Over the integers, consider x+(-9)=-5 with candidate x=4. After substitution into the original equation, is the candidate a solution?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"The left side is 4+(-9)=-5, while the right side is -5; the two sides are equal."},"skills":["verification by substitution","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-20260924-equation-solution-verification-0005","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fd359229c56d1a2637804972daf3d8134a1bfa10a49ba30b919af43d66809ea8","family_id":"qf-equation-solution-verification","seed":20260929,"semantic_template":"qf-equation-solution-verification/{\"a\":-8,\"b\":-4,\"candidate\":5,\"domain\":\"integers\",\"form\":\"x+a=b\"}"},"fields":{"title":"Checking a Candidate Solution by Substitution","stem":"Over the integers, consider x+(-8)=-4 with candidate x=5. After substitution into the original equation, is the candidate a solution?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"The left side is 5+(-8)=-3, while the right side is -4; the two sides are not equal."},"skills":["verification by substitution","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-20260924-equation-solution-verification-0006","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a52ec39db800ccb5a14b5636083d3f0dd7bcde992c41641cc116938a0a85e71c","family_id":"qf-equation-solution-verification","seed":20260930,"semantic_template":"qf-equation-solution-verification/{\"a\":-7,\"b\":-3,\"candidate\":4,\"domain\":\"integers\",\"form\":\"x+a=b\"}"},"fields":{"title":"Checking a Candidate Solution by Substitution","stem":"Over the integers, consider x+(-7)=-3 with candidate x=4. After substitution into the original equation, is the candidate a solution?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"The left side is 4+(-7)=-3, while the right side is -3; the two sides are equal."},"skills":["verification by substitution","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-20260924-equation-solution-verification-0007","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"366d79a67a9cc50a6103ad387a1a6d9b498a4d9d4624daf794e050303905cd19","family_id":"qf-equation-solution-verification","seed":20260931,"semantic_template":"qf-equation-solution-verification/{\"a\":-6,\"b\":-2,\"candidate\":5,\"domain\":\"integers\",\"form\":\"x+a=b\"}"},"fields":{"title":"Checking a Candidate Solution by Substitution","stem":"Over the integers, consider x+(-6)=-2 with candidate x=5. After substitution into the original equation, is the candidate a solution?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"The left side is 5+(-6)=-1, while the right side is -2; the two sides are not equal."},"skills":["verification by substitution","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-20260924-equation-solution-verification-0008","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9b3c386261ebcb74fca882e0556898625ea621f4d6bb100466c7c873819d4c4b","family_id":"qf-equation-solution-verification","seed":20260932,"semantic_template":"qf-equation-solution-verification/{\"a\":-5,\"b\":-1,\"candidate\":4,\"domain\":\"integers\",\"form\":\"x+a=b\"}"},"fields":{"title":"Checking a Candidate Solution by Substitution","stem":"Over the integers, consider x+(-5)=-1 with candidate x=4. After substitution into the original equation, is the candidate a solution?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"The left side is 4+(-5)=-1, while the right side is -1; the two sides are equal."},"skills":["verification by substitution","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-20260924-equation-solution-verification-0009","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0801aa70a88ccd46c82c690854e522f134e9987e9521ba7f55254ac469039f9d","family_id":"qf-equation-solution-verification","seed":20260933,"semantic_template":"qf-equation-solution-verification/{\"a\":-4,\"b\":0,\"candidate\":5,\"domain\":\"integers\",\"form\":\"x+a=b\"}"},"fields":{"title":"Checking a Candidate Solution by Substitution","stem":"Over the integers, consider x+(-4)=0 with candidate x=5. After substitution into the original equation, is the candidate a solution?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"The left side is 5+(-4)=1, while the right side is 0; the two sides are not equal."},"skills":["verification by substitution","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-20260924-equation-solution-verification-0010","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1276c667648da32e17bfda3e2df59800e2578e4e1859f5da882523b12bbff9db","family_id":"qf-equation-solution-verification","seed":20260934,"semantic_template":"qf-equation-solution-verification/{\"a\":-3,\"b\":1,\"candidate\":4,\"domain\":\"integers\",\"form\":\"x+a=b\"}"},"fields":{"title":"Checking a Candidate Solution by Substitution","stem":"Over the integers, consider x+(-3)=1 with candidate x=4. After substitution into the original equation, is the candidate a solution?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"The left side is 4+(-3)=1, while the right side is 1; the two sides are equal."},"skills":["verification by substitution","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-20260924-equation-solution-verification-0011","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1ec7344a9473306cb0ef39ed24a116862c088a71731c4e80c120865f27f46f91","family_id":"qf-equation-solution-verification","seed":20260935,"semantic_template":"qf-equation-solution-verification/{\"a\":-2,\"b\":2,\"candidate\":5,\"domain\":\"integers\",\"form\":\"x+a=b\"}"},"fields":{"title":"Checking a Candidate Solution by Substitution","stem":"Over the integers, consider x+(-2)=2 with candidate x=5. After substitution into the original equation, is the candidate a solution?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"The left side is 5+(-2)=3, while the right side is 2; the two sides are not equal."},"skills":["verification by substitution","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-20260924-equation-solution-verification-0012","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"340704755d560ec41d04fc599cf6e29523a33e7f7d2f998ef65fe14f432f587f","family_id":"qf-equation-solution-verification","seed":20260936,"semantic_template":"qf-equation-solution-verification/{\"a\":-1,\"b\":3,\"candidate\":4,\"domain\":\"integers\",\"form\":\"x+a=b\"}"},"fields":{"title":"Checking a Candidate Solution by Substitution","stem":"Over the integers, consider x+(-1)=3 with candidate x=4. After substitution into the original equation, is the candidate a solution?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"The left side is 4+(-1)=3, while the right side is 3; the two sides are equal."},"skills":["verification by substitution","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-20260924-equation-solution-verification-0013","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"063e64e4e81176551c9fd17fcc05d86aa897f58d1ad3c9369e3bf642a1d4a1f9","family_id":"qf-equation-solution-verification","seed":20260937,"semantic_template":"qf-equation-solution-verification/{\"a\":0,\"b\":4,\"candidate\":5,\"domain\":\"integers\",\"form\":\"x+a=b\"}"},"fields":{"title":"Checking a Candidate Solution by Substitution","stem":"Over the integers, consider x+(0)=4 with candidate x=5. After substitution into the original equation, is the candidate a solution?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"The left side is 5+(0)=5, while the right side is 4; the two sides are not equal."},"skills":["verification by substitution","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-20260924-equation-solution-verification-0014","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"42ade7b3666bfa995edca766893f5d9cb46e31205c677c6055a1490f0b490f4e","family_id":"qf-equation-solution-verification","seed":20260938,"semantic_template":"qf-equation-solution-verification/{\"a\":1,\"b\":5,\"candidate\":4,\"domain\":\"integers\",\"form\":\"x+a=b\"}"},"fields":{"title":"Checking a Candidate Solution by Substitution","stem":"Over the integers, consider x+(1)=5 with candidate x=4. After substitution into the original equation, is the candidate a solution?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"The left side is 4+(1)=5, while the right side is 5; the two sides are equal."},"skills":["verification by substitution","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-20260924-equation-solution-verification-0015","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"274d4308e7af94a0fa2e156f7f9981613d383928ccef44e832a6f39e82a7a59e","family_id":"qf-equation-solution-verification","seed":20260939,"semantic_template":"qf-equation-solution-verification/{\"a\":2,\"b\":6,\"candidate\":5,\"domain\":\"integers\",\"form\":\"x+a=b\"}"},"fields":{"title":"Checking a Candidate Solution by Substitution","stem":"Over the integers, consider x+(2)=6 with candidate x=5. After substitution into the original equation, is the candidate a solution?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"The left side is 5+(2)=7, while the right side is 6; the two sides are not equal."},"skills":["verification by substitution","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-20260924-equation-solution-verification-0016","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6ad3f95a35dc2a73604a2e4f49dae0170c59e2a05deffe4c98a4042b8231a783","family_id":"qf-equation-solution-verification","seed":20260940,"semantic_template":"qf-equation-solution-verification/{\"a\":3,\"b\":7,\"candidate\":4,\"domain\":\"integers\",\"form\":\"x+a=b\"}"},"fields":{"title":"Checking a Candidate Solution by Substitution","stem":"Over the integers, consider x+(3)=7 with candidate x=4. After substitution into the original equation, is the candidate a solution?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"The left side is 4+(3)=7, while the right side is 7; the two sides are equal."},"skills":["verification by substitution","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-20260924-equation-solution-verification-0017","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c50bd11b670f39ae0b772dc676670c4f500357de57110e93ab71d16ec0d6b5a3","family_id":"qf-equation-solution-verification","seed":20260941,"semantic_template":"qf-equation-solution-verification/{\"a\":4,\"b\":8,\"candidate\":5,\"domain\":\"integers\",\"form\":\"x+a=b\"}"},"fields":{"title":"Checking a Candidate Solution by Substitution","stem":"Over the integers, consider x+(4)=8 with candidate x=5. After substitution into the original equation, is the candidate a solution?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"The left side is 5+(4)=9, while the right side is 8; the two sides are not equal."},"skills":["verification by substitution","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-20260924-equation-solution-verification-0018","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4fc32f785ae8d9898a1bd0e52ad4fc4f92d56f496d8e5a3ba6480682f835eadb","family_id":"qf-equation-solution-verification","seed":20260942,"semantic_template":"qf-equation-solution-verification/{\"a\":5,\"b\":-8,\"candidate\":-13,\"domain\":\"integers\",\"form\":\"x+a=b\"}"},"fields":{"title":"Checking a Candidate Solution by Substitution","stem":"Over the integers, consider x+(5)=-8 with candidate x=-13. After substitution into the original equation, is the candidate a solution?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"The left side is -13+(5)=-8, while the right side is -8; the two sides are equal."},"skills":["verification by substitution","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-20260924-equation-solution-verification-0019","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ada3c83b86ee7f3c4cb67b9759dd7378d92b72bb42a0add7c052566c85b29f4b","family_id":"qf-equation-solution-verification","seed":20260943,"semantic_template":"qf-equation-solution-verification/{\"a\":6,\"b\":-7,\"candidate\":-12,\"domain\":\"integers\",\"form\":\"x+a=b\"}"},"fields":{"title":"Checking a Candidate Solution by Substitution","stem":"Over the integers, consider x+(6)=-7 with candidate x=-12. After substitution into the original equation, is the candidate a solution?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"The left side is -12+(6)=-6, while the right side is -7; the two sides are not equal."},"skills":["verification by substitution","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-20260924-equation-solution-verification-0020","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f5bc7fa4f99a4236a58434ececa038f763ec10905e84ef2ce257a15d99b7c4a0","family_id":"qf-equation-solution-verification","seed":20260944,"semantic_template":"qf-equation-solution-verification/{\"a\":7,\"b\":-6,\"candidate\":-13,\"domain\":\"integers\",\"form\":\"x+a=b\"}"},"fields":{"title":"Checking a Candidate Solution by Substitution","stem":"Over the integers, consider x+(7)=-6 with candidate x=-13. After substitution into the original equation, is the candidate a solution?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"The left side is -13+(7)=-6, while the right side is -6; the two sides are equal."},"skills":["verification by substitution","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-20260924-equation-solution-verification-0021","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c1d8fa89b3849e38ed273b607d998900f72edd04a1eb05c918d9c4bbbc373e11","family_id":"qf-equation-solution-verification","seed":20260945,"semantic_template":"qf-equation-solution-verification/{\"a\":8,\"b\":-5,\"candidate\":-12,\"domain\":\"integers\",\"form\":\"x+a=b\"}"},"fields":{"title":"Checking a Candidate Solution by Substitution","stem":"Over the integers, consider x+(8)=-5 with candidate x=-12. After substitution into the original equation, is the candidate a solution?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"The left side is -12+(8)=-4, while the right side is -5; the two sides are not equal."},"skills":["verification by substitution","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-20260924-equation-solution-verification-0022","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"969d2c2e97b4068db3ebc30cd2df382807738707cadaef2413338f649126b8c0","family_id":"qf-equation-solution-verification","seed":20260946,"semantic_template":"qf-equation-solution-verification/{\"a\":9,\"b\":-4,\"candidate\":-13,\"domain\":\"integers\",\"form\":\"x+a=b\"}"},"fields":{"title":"Checking a Candidate Solution by Substitution","stem":"Over the integers, consider x+(9)=-4 with candidate x=-13. After substitution into the original equation, is the candidate a solution?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"The left side is -13+(9)=-4, while the right side is -4; the two sides are equal."},"skills":["verification by substitution","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-20260924-equation-solution-verification-0023","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"258c670e27f3f393cd6fdabdb167f33da373bb0cc7e271f931fd6758c4ee3eaa","family_id":"qf-equation-solution-verification","seed":20260947,"semantic_template":"qf-equation-solution-verification/{\"a\":10,\"b\":-3,\"candidate\":-12,\"domain\":\"integers\",\"form\":\"x+a=b\"}"},"fields":{"title":"Checking a Candidate Solution by Substitution","stem":"Over the integers, consider x+(10)=-3 with candidate x=-12. After substitution into the original equation, is the candidate a solution?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"The left side is -12+(10)=-2, while the right side is -3; the two sides are not equal."},"skills":["verification by substitution","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-20260924-equation-solution-verification-0024","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"00d225b6efb1d343c8c32413ec9d8f48089ae90cab923344ddfc8b840511e64f","family_id":"qf-equation-solution-verification","seed":20260948,"semantic_template":"qf-equation-solution-verification/{\"a\":11,\"b\":-2,\"candidate\":-13,\"domain\":\"integers\",\"form\":\"x+a=b\"}"},"fields":{"title":"Checking a Candidate Solution by Substitution","stem":"Over the integers, consider x+(11)=-2 with candidate x=-13. After substitution into the original equation, is the candidate a solution?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"The left side is -13+(11)=-2, while the right side is -2; the two sides are equal."},"skills":["verification by substitution","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-20260924-equation-solution-verification-0025","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"54c8655f8074e3f4eb46c7aeb0a4d958363d0088bdc94980df39d7a06f5ae762","family_id":"qf-equation-solution-verification","seed":20260949,"semantic_template":"qf-equation-solution-verification/{\"a\":12,\"b\":-1,\"candidate\":-12,\"domain\":\"integers\",\"form\":\"x+a=b\"}"},"fields":{"title":"Checking a Candidate Solution by Substitution","stem":"Over the integers, consider x+(12)=-1 with candidate x=-12. After substitution into the original equation, is the candidate a solution?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"The left side is -12+(12)=0, while the right side is -1; the two sides are not equal."},"skills":["verification by substitution","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-20260924-equation-additive-solve-0001","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9441ff5c81523a1675d7a6bdfb1a1fe14ddd371a94cde6e8aa2999443f087a68","family_id":"qf-equation-additive-solve","seed":20261025,"semantic_template":"qf-equation-additive-solve/{\"a\":-15,\"b\":20,\"domain\":\"integers\",\"form\":\"x+a=b\"}"},"fields":{"title":"Additive Equation","stem":"Solve x+(-15)=20 over the integers.","answer":{"kind":"short_text","value":"35","explanation":"x=20−(-15)=35; substituting back satisfies the original equation."},"skills":["inverse addition","equations"],"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-20260924-equation-additive-solve-0002","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"93c17552a6716151aeb85baaac4a2bea53f18023cb51f5175b39ff93f09a14e2","family_id":"qf-equation-additive-solve","seed":20261026,"semantic_template":"qf-equation-additive-solve/{\"a\":-14,\"b\":19,\"domain\":\"integers\",\"form\":\"x+a=b\"}"},"fields":{"title":"Additive Equation","stem":"Solve x+(-14)=19 over the integers.","answer":{"kind":"short_text","value":"33","explanation":"x=19−(-14)=33; substituting back satisfies the original equation."},"skills":["inverse addition","equations"],"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-20260924-equation-additive-solve-0003","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2bfea0db05ee52207b015f286bd6419a122332c3f1bdc23c50de2d32489fe64e","family_id":"qf-equation-additive-solve","seed":20261027,"semantic_template":"qf-equation-additive-solve/{\"a\":-13,\"b\":18,\"domain\":\"integers\",\"form\":\"x+a=b\"}"},"fields":{"title":"Additive Equation","stem":"Solve x+(-13)=18 over the integers.","answer":{"kind":"short_text","value":"31","explanation":"x=18−(-13)=31; substituting back satisfies the original equation."},"skills":["inverse addition","equations"],"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-20260924-equation-additive-solve-0004","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0134e240653a9653d4641eb383f5d2410904b608ce1a2a29b89cf6a0d9c074bc","family_id":"qf-equation-additive-solve","seed":20261028,"semantic_template":"qf-equation-additive-solve/{\"a\":-12,\"b\":17,\"domain\":\"integers\",\"form\":\"x+a=b\"}"},"fields":{"title":"Additive Equation","stem":"Solve x+(-12)=17 over the integers.","answer":{"kind":"short_text","value":"29","explanation":"x=17−(-12)=29; substituting back satisfies the original equation."},"skills":["inverse addition","equations"],"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-20260924-equation-additive-solve-0005","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fc5f581cda68e995599de0c9d4e546c79390a785f255464f09d8a858bd5aa074","family_id":"qf-equation-additive-solve","seed":20261029,"semantic_template":"qf-equation-additive-solve/{\"a\":-11,\"b\":16,\"domain\":\"integers\",\"form\":\"x+a=b\"}"},"fields":{"title":"Additive Equation","stem":"Solve x+(-11)=16 over the integers.","answer":{"kind":"short_text","value":"27","explanation":"x=16−(-11)=27; substituting back satisfies the original equation."},"skills":["inverse addition","equations"],"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-20260924-equation-additive-solve-0006","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"625ca9d0086bfc47f0b3c77b320d9f67a52be97f91ce4f68d255ed22a5850148","family_id":"qf-equation-additive-solve","seed":20261030,"semantic_template":"qf-equation-additive-solve/{\"a\":-10,\"b\":15,\"domain\":\"integers\",\"form\":\"x+a=b\"}"},"fields":{"title":"Additive Equation","stem":"Solve x+(-10)=15 over the integers.","answer":{"kind":"short_text","value":"25","explanation":"x=15−(-10)=25; substituting back satisfies the original equation."},"skills":["inverse addition","equations"],"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-20260924-equation-additive-solve-0007","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e26e73fc9cceeef820459671c6e82f094c6baa1999ef09a878f941ef1c49c08b","family_id":"qf-equation-additive-solve","seed":20261031,"semantic_template":"qf-equation-additive-solve/{\"a\":-9,\"b\":14,\"domain\":\"integers\",\"form\":\"x+a=b\"}"},"fields":{"title":"Additive Equation","stem":"Solve x+(-9)=14 over the integers.","answer":{"kind":"short_text","value":"23","explanation":"x=14−(-9)=23; substituting back satisfies the original equation."},"skills":["inverse addition","equations"],"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-20260924-equation-additive-solve-0008","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"70a7f50f1c0aa5a0ca0134483b6e635207cbe8f22266fe9badc52addbf1756ab","family_id":"qf-equation-additive-solve","seed":20261032,"semantic_template":"qf-equation-additive-solve/{\"a\":-8,\"b\":13,\"domain\":\"integers\",\"form\":\"x+a=b\"}"},"fields":{"title":"Additive Equation","stem":"Solve x+(-8)=13 over the integers.","answer":{"kind":"short_text","value":"21","explanation":"x=13−(-8)=21; substituting back satisfies the original equation."},"skills":["inverse addition","equations"],"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-20260924-equation-additive-solve-0009","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b46fa39f20952add64283967357bef5c1457419db447c46fd2dbcea6e950f5ca","family_id":"qf-equation-additive-solve","seed":20261033,"semantic_template":"qf-equation-additive-solve/{\"a\":-7,\"b\":12,\"domain\":\"integers\",\"form\":\"x+a=b\"}"},"fields":{"title":"Additive Equation","stem":"Solve x+(-7)=12 over the integers.","answer":{"kind":"short_text","value":"19","explanation":"x=12−(-7)=19; substituting back satisfies the original equation."},"skills":["inverse addition","equations"],"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-20260924-equation-additive-solve-0010","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1587302e4e467d79bed33658316cd6118f83321888b0561f4b36e539d2bf41a1","family_id":"qf-equation-additive-solve","seed":20261034,"semantic_template":"qf-equation-additive-solve/{\"a\":-6,\"b\":11,\"domain\":\"integers\",\"form\":\"x+a=b\"}"},"fields":{"title":"Additive Equation","stem":"Solve x+(-6)=11 over the integers.","answer":{"kind":"short_text","value":"17","explanation":"x=11−(-6)=17; substituting back satisfies the original equation."},"skills":["inverse addition","equations"],"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-20260924-equation-additive-solve-0011","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"88172105cc09d7cf510a91131e1581173030338f116e66100b8b980d452c7355","family_id":"qf-equation-additive-solve","seed":20261035,"semantic_template":"qf-equation-additive-solve/{\"a\":-5,\"b\":10,\"domain\":\"integers\",\"form\":\"x+a=b\"}"},"fields":{"title":"Additive Equation","stem":"Solve x+(-5)=10 over the integers.","answer":{"kind":"short_text","value":"15","explanation":"x=10−(-5)=15; substituting back satisfies the original equation."},"skills":["inverse addition","equations"],"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-20260924-equation-additive-solve-0012","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4daba5a943d03f6f7737478f104a523104be0d22b920ed3acb47b02508699840","family_id":"qf-equation-additive-solve","seed":20261036,"semantic_template":"qf-equation-additive-solve/{\"a\":-4,\"b\":9,\"domain\":\"integers\",\"form\":\"x+a=b\"}"},"fields":{"title":"Additive Equation","stem":"Solve x+(-4)=9 over the integers.","answer":{"kind":"short_text","value":"13","explanation":"x=9−(-4)=13; substituting back satisfies the original equation."},"skills":["inverse addition","equations"],"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-20260924-equation-additive-solve-0013","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1d0820b7b82003952cb48a84939a2ef73d9d1e745b0a6f94a003da31b498f7ee","family_id":"qf-equation-additive-solve","seed":20261037,"semantic_template":"qf-equation-additive-solve/{\"a\":-3,\"b\":8,\"domain\":\"integers\",\"form\":\"x+a=b\"}"},"fields":{"title":"Additive Equation","stem":"Solve x+(-3)=8 over the integers.","answer":{"kind":"short_text","value":"11","explanation":"x=8−(-3)=11; substituting back satisfies the original equation."},"skills":["inverse addition","equations"],"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-20260924-equation-additive-solve-0014","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3494b8e498d1e459af1793f0eae905e327f4ac7d8d6db880b3220f5ff9a1fe9e","family_id":"qf-equation-additive-solve","seed":20261038,"semantic_template":"qf-equation-additive-solve/{\"a\":-2,\"b\":7,\"domain\":\"integers\",\"form\":\"x+a=b\"}"},"fields":{"title":"Additive Equation","stem":"Solve x+(-2)=7 over the integers.","answer":{"kind":"short_text","value":"9","explanation":"x=7−(-2)=9; substituting back satisfies the original equation."},"skills":["inverse addition","equations"],"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-20260924-equation-additive-solve-0015","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"af73f392fa03648762c251509c60099b719099467949c7e91cf59f94100bb547","family_id":"qf-equation-additive-solve","seed":20261039,"semantic_template":"qf-equation-additive-solve/{\"a\":-1,\"b\":6,\"domain\":\"integers\",\"form\":\"x+a=b\"}"},"fields":{"title":"Additive Equation","stem":"Solve x+(-1)=6 over the integers.","answer":{"kind":"short_text","value":"7","explanation":"x=6−(-1)=7; substituting back satisfies the original equation."},"skills":["inverse addition","equations"],"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-20260924-equation-additive-solve-0016","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"56db8b264138084b07e5b64beebfb96a9df15baa4972f8453e2bef403d086cb4","family_id":"qf-equation-additive-solve","seed":20261040,"semantic_template":"qf-equation-additive-solve/{\"a\":0,\"b\":5,\"domain\":\"integers\",\"form\":\"x+a=b\"}"},"fields":{"title":"Additive Equation","stem":"Solve x+(0)=5 over the integers.","answer":{"kind":"short_text","value":"5","explanation":"x=5−(0)=5; substituting back satisfies the original equation."},"skills":["inverse addition","equations"],"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-20260924-equation-additive-solve-0017","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"842188080dc36f27271402b6893646d41d3124e6b90561a026fd115b89fce1ca","family_id":"qf-equation-additive-solve","seed":20261041,"semantic_template":"qf-equation-additive-solve/{\"a\":1,\"b\":4,\"domain\":\"integers\",\"form\":\"x+a=b\"}"},"fields":{"title":"Additive Equation","stem":"Solve x+(1)=4 over the integers.","answer":{"kind":"short_text","value":"3","explanation":"x=4−(1)=3; substituting back satisfies the original equation."},"skills":["inverse addition","equations"],"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-20260924-equation-additive-solve-0018","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9d98165bdccd2d8cb85ce8d96512eac18f945e3b16f9629f51bd945b00d2d102","family_id":"qf-equation-additive-solve","seed":20261042,"semantic_template":"qf-equation-additive-solve/{\"a\":2,\"b\":3,\"domain\":\"integers\",\"form\":\"x+a=b\"}"},"fields":{"title":"Additive Equation","stem":"Solve x+(2)=3 over the integers.","answer":{"kind":"short_text","value":"1","explanation":"x=3−(2)=1; substituting back satisfies the original equation."},"skills":["inverse addition","equations"],"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-20260924-equation-additive-solve-0019","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"bbafec664736ef17eb742552a77b1750db6d9cd6544d51c740682706e77c726c","family_id":"qf-equation-additive-solve","seed":20261043,"semantic_template":"qf-equation-additive-solve/{\"a\":3,\"b\":2,\"domain\":\"integers\",\"form\":\"x+a=b\"}"},"fields":{"title":"Additive Equation","stem":"Solve x+(3)=2 over the integers.","answer":{"kind":"short_text","value":"-1","explanation":"x=2−(3)=-1; substituting back satisfies the original equation."},"skills":["inverse addition","equations"],"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-20260924-equation-additive-solve-0020","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a0530a8df33407943bfa272e3409d0a7673610e85deb2633696b94ffcd82ddda","family_id":"qf-equation-additive-solve","seed":20261044,"semantic_template":"qf-equation-additive-solve/{\"a\":4,\"b\":1,\"domain\":\"integers\",\"form\":\"x+a=b\"}"},"fields":{"title":"Additive Equation","stem":"Solve x+(4)=1 over the integers.","answer":{"kind":"short_text","value":"-3","explanation":"x=1−(4)=-3; substituting back satisfies the original equation."},"skills":["inverse addition","equations"],"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-20260924-equation-additive-solve-0021","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7103ac1f7024b42c7ec1c204507ba74ec472c584ddca32e52fd521883287da55","family_id":"qf-equation-additive-solve","seed":20261045,"semantic_template":"qf-equation-additive-solve/{\"a\":5,\"b\":0,\"domain\":\"integers\",\"form\":\"x+a=b\"}"},"fields":{"title":"Additive Equation","stem":"Solve x+(5)=0 over the integers.","answer":{"kind":"short_text","value":"-5","explanation":"x=0−(5)=-5; substituting back satisfies the original equation."},"skills":["inverse addition","equations"],"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-20260924-equation-additive-solve-0022","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e141e8fa57ced0d21ba98c6515b7b4f0fc26a02a738cd6f4db37497d3346721d","family_id":"qf-equation-additive-solve","seed":20261046,"semantic_template":"qf-equation-additive-solve/{\"a\":6,\"b\":-1,\"domain\":\"integers\",\"form\":\"x+a=b\"}"},"fields":{"title":"Additive Equation","stem":"Solve x+(6)=-1 over the integers.","answer":{"kind":"short_text","value":"-7","explanation":"x=-1−(6)=-7; substituting back satisfies the original equation."},"skills":["inverse addition","equations"],"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-20260924-equation-additive-solve-0023","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"baed1463fe2a6271032108c7e2e05b07771bcbd04ac8fd553f4ec5f529ae5453","family_id":"qf-equation-additive-solve","seed":20261047,"semantic_template":"qf-equation-additive-solve/{\"a\":7,\"b\":-2,\"domain\":\"integers\",\"form\":\"x+a=b\"}"},"fields":{"title":"Additive Equation","stem":"Solve x+(7)=-2 over the integers.","answer":{"kind":"short_text","value":"-9","explanation":"x=-2−(7)=-9; substituting back satisfies the original equation."},"skills":["inverse addition","equations"],"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-20260924-equation-additive-solve-0024","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"cffbeddc5cad2b79293217bdf8717cf99ae615a128b8955b54db20983ae38985","family_id":"qf-equation-additive-solve","seed":20261048,"semantic_template":"qf-equation-additive-solve/{\"a\":8,\"b\":-3,\"domain\":\"integers\",\"form\":\"x+a=b\"}"},"fields":{"title":"Additive Equation","stem":"Solve x+(8)=-3 over the integers.","answer":{"kind":"short_text","value":"-11","explanation":"x=-3−(8)=-11; substituting back satisfies the original equation."},"skills":["inverse addition","equations"],"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-20260924-equation-additive-solve-0025","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3aa46cff6878189d257f913e53a05747d4094be33919c08c64f4d58d1c5d008f","family_id":"qf-equation-additive-solve","seed":20261049,"semantic_template":"qf-equation-additive-solve/{\"a\":9,\"b\":-4,\"domain\":\"integers\",\"form\":\"x+a=b\"}"},"fields":{"title":"Additive Equation","stem":"Solve x+(9)=-4 over the integers.","answer":{"kind":"short_text","value":"-13","explanation":"x=-4−(9)=-13; substituting back satisfies the original equation."},"skills":["inverse addition","equations"],"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-20260924-equation-multiplicative-solve-0001","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1b02508c5395ffc2bcd6447428abb0cea20dbc69127ea3543989c2df482a18d0","family_id":"qf-equation-multiplicative-solve","seed":20261125,"semantic_template":"qf-equation-multiplicative-solve/{\"a\":1,\"b\":-5,\"domain\":\"integers\",\"form\":\"a*x=b\"}"},"fields":{"title":"Multiplicative Equation","stem":"Solve 1×x=-5 over the integers; the coefficient 1 is explicitly nonzero.","answer":{"kind":"short_text","value":"-5","explanation":"1≠0, so x=-5/1=-5; substitution verifies the equality."},"skills":["nonzero coefficient","inverse 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-20260924-equation-multiplicative-solve-0002","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e318a5e733f95a3553a8696d702f5ae5fffa99298a81cb80f6e63c3c14a48b3d","family_id":"qf-equation-multiplicative-solve","seed":20261126,"semantic_template":"qf-equation-multiplicative-solve/{\"a\":2,\"b\":-8,\"domain\":\"integers\",\"form\":\"a*x=b\"}"},"fields":{"title":"Multiplicative Equation","stem":"Solve 2×x=-8 over the integers; the coefficient 2 is explicitly nonzero.","answer":{"kind":"short_text","value":"-4","explanation":"2≠0, so x=-8/2=-4; substitution verifies the equality."},"skills":["nonzero coefficient","inverse 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-20260924-equation-multiplicative-solve-0003","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ccad2bd97e8778cea6236f7f9330b7f0d904326558fc0719465d96885260c8b3","family_id":"qf-equation-multiplicative-solve","seed":20261127,"semantic_template":"qf-equation-multiplicative-solve/{\"a\":3,\"b\":-9,\"domain\":\"integers\",\"form\":\"a*x=b\"}"},"fields":{"title":"Multiplicative Equation","stem":"Solve 3×x=-9 over the integers; the coefficient 3 is explicitly nonzero.","answer":{"kind":"short_text","value":"-3","explanation":"3≠0, so x=-9/3=-3; substitution verifies the equality."},"skills":["nonzero coefficient","inverse 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-20260924-equation-multiplicative-solve-0004","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"203aedb84393df54e64e29adac6ad3fe5d014989cd67816132269de8e18d64bf","family_id":"qf-equation-multiplicative-solve","seed":20261128,"semantic_template":"qf-equation-multiplicative-solve/{\"a\":4,\"b\":-8,\"domain\":\"integers\",\"form\":\"a*x=b\"}"},"fields":{"title":"Multiplicative Equation","stem":"Solve 4×x=-8 over the integers; the coefficient 4 is explicitly nonzero.","answer":{"kind":"short_text","value":"-2","explanation":"4≠0, so x=-8/4=-2; substitution verifies the equality."},"skills":["nonzero coefficient","inverse 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-20260924-equation-multiplicative-solve-0005","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"97d34953e2a7ac34c9f069ba14325622669bc102629999f04d05d64295599066","family_id":"qf-equation-multiplicative-solve","seed":20261129,"semantic_template":"qf-equation-multiplicative-solve/{\"a\":5,\"b\":-5,\"domain\":\"integers\",\"form\":\"a*x=b\"}"},"fields":{"title":"Multiplicative Equation","stem":"Solve 5×x=-5 over the integers; the coefficient 5 is explicitly nonzero.","answer":{"kind":"short_text","value":"-1","explanation":"5≠0, so x=-5/5=-1; substitution verifies the equality."},"skills":["nonzero coefficient","inverse 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-20260924-equation-multiplicative-solve-0006","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c7398a69d73d62a74d724385291720982ee9594a4232a21612c784b0d0e73b30","family_id":"qf-equation-multiplicative-solve","seed":20261130,"semantic_template":"qf-equation-multiplicative-solve/{\"a\":6,\"b\":0,\"domain\":\"integers\",\"form\":\"a*x=b\"}"},"fields":{"title":"Multiplicative Equation","stem":"Solve 6×x=0 over the integers; the coefficient 6 is explicitly nonzero.","answer":{"kind":"short_text","value":"0","explanation":"6≠0, so x=0/6=0; substitution verifies the equality."},"skills":["nonzero coefficient","inverse 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-20260924-equation-multiplicative-solve-0007","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e18ab20d10c19f9499cb37280b30c21d1466cc17dfd14f7db295913524ac6243","family_id":"qf-equation-multiplicative-solve","seed":20261131,"semantic_template":"qf-equation-multiplicative-solve/{\"a\":7,\"b\":7,\"domain\":\"integers\",\"form\":\"a*x=b\"}"},"fields":{"title":"Multiplicative Equation","stem":"Solve 7×x=7 over the integers; the coefficient 7 is explicitly nonzero.","answer":{"kind":"short_text","value":"1","explanation":"7≠0, so x=7/7=1; substitution verifies the equality."},"skills":["nonzero coefficient","inverse 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-20260924-equation-multiplicative-solve-0008","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6f37ae611611b39b3ea3e4c4a7283ab0bc66c38c5e27f6f6b1a7733927ae4c3c","family_id":"qf-equation-multiplicative-solve","seed":20261132,"semantic_template":"qf-equation-multiplicative-solve/{\"a\":8,\"b\":16,\"domain\":\"integers\",\"form\":\"a*x=b\"}"},"fields":{"title":"Multiplicative Equation","stem":"Solve 8×x=16 over the integers; the coefficient 8 is explicitly nonzero.","answer":{"kind":"short_text","value":"2","explanation":"8≠0, so x=16/8=2; substitution verifies the equality."},"skills":["nonzero coefficient","inverse 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-20260924-equation-multiplicative-solve-0009","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d674fca06329058f283210593c33443195c0b21eba0f591eb9718fbdae34eb49","family_id":"qf-equation-multiplicative-solve","seed":20261133,"semantic_template":"qf-equation-multiplicative-solve/{\"a\":9,\"b\":27,\"domain\":\"integers\",\"form\":\"a*x=b\"}"},"fields":{"title":"Multiplicative Equation","stem":"Solve 9×x=27 over the integers; the coefficient 9 is explicitly nonzero.","answer":{"kind":"short_text","value":"3","explanation":"9≠0, so x=27/9=3; substitution verifies the equality."},"skills":["nonzero coefficient","inverse 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-20260924-equation-multiplicative-solve-0010","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f098a776f77d5a17698f72145a1d656846ac81c9e3c2ec99595c45132ab487cc","family_id":"qf-equation-multiplicative-solve","seed":20261134,"semantic_template":"qf-equation-multiplicative-solve/{\"a\":1,\"b\":4,\"domain\":\"integers\",\"form\":\"a*x=b\"}"},"fields":{"title":"Multiplicative Equation","stem":"Solve 1×x=4 over the integers; the coefficient 1 is explicitly nonzero.","answer":{"kind":"short_text","value":"4","explanation":"1≠0, so x=4/1=4; substitution verifies the equality."},"skills":["nonzero coefficient","inverse 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-20260924-equation-multiplicative-solve-0011","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6d51525fa0cb250839ea39a7a4da41381b196cbab0dad2093ac5ea85e0b7e37f","family_id":"qf-equation-multiplicative-solve","seed":20261135,"semantic_template":"qf-equation-multiplicative-solve/{\"a\":2,\"b\":10,\"domain\":\"integers\",\"form\":\"a*x=b\"}"},"fields":{"title":"Multiplicative Equation","stem":"Solve 2×x=10 over the integers; the coefficient 2 is explicitly nonzero.","answer":{"kind":"short_text","value":"5","explanation":"2≠0, so x=10/2=5; substitution verifies the equality."},"skills":["nonzero coefficient","inverse 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-20260924-equation-multiplicative-solve-0012","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f3fb9061cfc2b6a1efb70c91dbc3a8da4bef4cba71ead162fad3d709b5509147","family_id":"qf-equation-multiplicative-solve","seed":20261136,"semantic_template":"qf-equation-multiplicative-solve/{\"a\":3,\"b\":-15,\"domain\":\"integers\",\"form\":\"a*x=b\"}"},"fields":{"title":"Multiplicative Equation","stem":"Solve 3×x=-15 over the integers; the coefficient 3 is explicitly nonzero.","answer":{"kind":"short_text","value":"-5","explanation":"3≠0, so x=-15/3=-5; substitution verifies the equality."},"skills":["nonzero coefficient","inverse 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-20260924-equation-multiplicative-solve-0013","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"720d2d601357cb915626f69a46234ada25fea2b2288acfbca20b85485631efa1","family_id":"qf-equation-multiplicative-solve","seed":20261137,"semantic_template":"qf-equation-multiplicative-solve/{\"a\":4,\"b\":-16,\"domain\":\"integers\",\"form\":\"a*x=b\"}"},"fields":{"title":"Multiplicative Equation","stem":"Solve 4×x=-16 over the integers; the coefficient 4 is explicitly nonzero.","answer":{"kind":"short_text","value":"-4","explanation":"4≠0, so x=-16/4=-4; substitution verifies the equality."},"skills":["nonzero coefficient","inverse 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-20260924-equation-multiplicative-solve-0014","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5194c3ab2f90e70a83bafe591a09fa7bdc1f588b4800ec94c93f64300017d14f","family_id":"qf-equation-multiplicative-solve","seed":20261138,"semantic_template":"qf-equation-multiplicative-solve/{\"a\":5,\"b\":-15,\"domain\":\"integers\",\"form\":\"a*x=b\"}"},"fields":{"title":"Multiplicative Equation","stem":"Solve 5×x=-15 over the integers; the coefficient 5 is explicitly nonzero.","answer":{"kind":"short_text","value":"-3","explanation":"5≠0, so x=-15/5=-3; substitution verifies the equality."},"skills":["nonzero coefficient","inverse 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-20260924-equation-multiplicative-solve-0015","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ef989f9fe80dfb4b55089c5cae73150447eaabd25f95fb670275363c858717ae","family_id":"qf-equation-multiplicative-solve","seed":20261139,"semantic_template":"qf-equation-multiplicative-solve/{\"a\":6,\"b\":-12,\"domain\":\"integers\",\"form\":\"a*x=b\"}"},"fields":{"title":"Multiplicative Equation","stem":"Solve 6×x=-12 over the integers; the coefficient 6 is explicitly nonzero.","answer":{"kind":"short_text","value":"-2","explanation":"6≠0, so x=-12/6=-2; substitution verifies the equality."},"skills":["nonzero coefficient","inverse 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-20260924-equation-multiplicative-solve-0016","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3bd2f31926e74dcda12aec88b917778b27cca4b19596fa894df355cca3c5c3a6","family_id":"qf-equation-multiplicative-solve","seed":20261140,"semantic_template":"qf-equation-multiplicative-solve/{\"a\":7,\"b\":-7,\"domain\":\"integers\",\"form\":\"a*x=b\"}"},"fields":{"title":"Multiplicative Equation","stem":"Solve 7×x=-7 over the integers; the coefficient 7 is explicitly nonzero.","answer":{"kind":"short_text","value":"-1","explanation":"7≠0, so x=-7/7=-1; substitution verifies the equality."},"skills":["nonzero coefficient","inverse 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-20260924-equation-multiplicative-solve-0017","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ce2105d9ec5fb2ae771f43fdf72954c9d54ff72548c1bc70ee8b8af4ef25cc5e","family_id":"qf-equation-multiplicative-solve","seed":20261141,"semantic_template":"qf-equation-multiplicative-solve/{\"a\":8,\"b\":0,\"domain\":\"integers\",\"form\":\"a*x=b\"}"},"fields":{"title":"Multiplicative Equation","stem":"Solve 8×x=0 over the integers; the coefficient 8 is explicitly nonzero.","answer":{"kind":"short_text","value":"0","explanation":"8≠0, so x=0/8=0; substitution verifies the equality."},"skills":["nonzero coefficient","inverse 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-20260924-equation-multiplicative-solve-0018","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"315e41207d98427efbb33e2e923b16016c82853bc7d343b68751d8941f3bb07d","family_id":"qf-equation-multiplicative-solve","seed":20261142,"semantic_template":"qf-equation-multiplicative-solve/{\"a\":9,\"b\":9,\"domain\":\"integers\",\"form\":\"a*x=b\"}"},"fields":{"title":"Multiplicative Equation","stem":"Solve 9×x=9 over the integers; the coefficient 9 is explicitly nonzero.","answer":{"kind":"short_text","value":"1","explanation":"9≠0, so x=9/9=1; substitution verifies the equality."},"skills":["nonzero coefficient","inverse 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-20260924-equation-multiplicative-solve-0019","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1bb20acbf6f5ceb1d9534064d893cc0eff4f0ccc384859a204ab4d16e321f182","family_id":"qf-equation-multiplicative-solve","seed":20261143,"semantic_template":"qf-equation-multiplicative-solve/{\"a\":1,\"b\":2,\"domain\":\"integers\",\"form\":\"a*x=b\"}"},"fields":{"title":"Multiplicative Equation","stem":"Solve 1×x=2 over the integers; the coefficient 1 is explicitly nonzero.","answer":{"kind":"short_text","value":"2","explanation":"1≠0, so x=2/1=2; substitution verifies the equality."},"skills":["nonzero coefficient","inverse 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-20260924-equation-multiplicative-solve-0020","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"24b512bd3d747f1e0ecc29e6780786b83ce9032f6f6f45e3d7aef48bac6ac672","family_id":"qf-equation-multiplicative-solve","seed":20261144,"semantic_template":"qf-equation-multiplicative-solve/{\"a\":2,\"b\":6,\"domain\":\"integers\",\"form\":\"a*x=b\"}"},"fields":{"title":"Multiplicative Equation","stem":"Solve 2×x=6 over the integers; the coefficient 2 is explicitly nonzero.","answer":{"kind":"short_text","value":"3","explanation":"2≠0, so x=6/2=3; substitution verifies the equality."},"skills":["nonzero coefficient","inverse 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-20260924-equation-multiplicative-solve-0021","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"74334ba1b2168f5d9715ed83cd30b6d64a0ba68ec8258ed8418e58af0f3f1761","family_id":"qf-equation-multiplicative-solve","seed":20261145,"semantic_template":"qf-equation-multiplicative-solve/{\"a\":3,\"b\":12,\"domain\":\"integers\",\"form\":\"a*x=b\"}"},"fields":{"title":"Multiplicative Equation","stem":"Solve 3×x=12 over the integers; the coefficient 3 is explicitly nonzero.","answer":{"kind":"short_text","value":"4","explanation":"3≠0, so x=12/3=4; substitution verifies the equality."},"skills":["nonzero coefficient","inverse 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-20260924-equation-multiplicative-solve-0022","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6ca547adfc099f6becd4db375dab573bd7ea5e4ad46caaa83cf569f3d3b4185c","family_id":"qf-equation-multiplicative-solve","seed":20261146,"semantic_template":"qf-equation-multiplicative-solve/{\"a\":4,\"b\":20,\"domain\":\"integers\",\"form\":\"a*x=b\"}"},"fields":{"title":"Multiplicative Equation","stem":"Solve 4×x=20 over the integers; the coefficient 4 is explicitly nonzero.","answer":{"kind":"short_text","value":"5","explanation":"4≠0, so x=20/4=5; substitution verifies the equality."},"skills":["nonzero coefficient","inverse 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-20260924-equation-multiplicative-solve-0023","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"87c7bb099581a398ed40df488f4c0d2a05e956fac63a9419c88f8af07489d3fd","family_id":"qf-equation-multiplicative-solve","seed":20261147,"semantic_template":"qf-equation-multiplicative-solve/{\"a\":5,\"b\":-25,\"domain\":\"integers\",\"form\":\"a*x=b\"}"},"fields":{"title":"Multiplicative Equation","stem":"Solve 5×x=-25 over the integers; the coefficient 5 is explicitly nonzero.","answer":{"kind":"short_text","value":"-5","explanation":"5≠0, so x=-25/5=-5; substitution verifies the equality."},"skills":["nonzero coefficient","inverse 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-20260924-equation-multiplicative-solve-0024","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0770e061c628e07a4ff26dc231628506c7d54f135c2461ef4e135a5ce07174bc","family_id":"qf-equation-multiplicative-solve","seed":20261148,"semantic_template":"qf-equation-multiplicative-solve/{\"a\":6,\"b\":-24,\"domain\":\"integers\",\"form\":\"a*x=b\"}"},"fields":{"title":"Multiplicative Equation","stem":"Solve 6×x=-24 over the integers; the coefficient 6 is explicitly nonzero.","answer":{"kind":"short_text","value":"-4","explanation":"6≠0, so x=-24/6=-4; substitution verifies the equality."},"skills":["nonzero coefficient","inverse 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-20260924-equation-multiplicative-solve-0025","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7ff0f6074c318b95ed8a149e19fa2d3cea2019f8aaaea5cf88442ccacb150248","family_id":"qf-equation-multiplicative-solve","seed":20261149,"semantic_template":"qf-equation-multiplicative-solve/{\"a\":7,\"b\":-21,\"domain\":\"integers\",\"form\":\"a*x=b\"}"},"fields":{"title":"Multiplicative Equation","stem":"Solve 7×x=-21 over the integers; the coefficient 7 is explicitly nonzero.","answer":{"kind":"short_text","value":"-3","explanation":"7≠0, so x=-21/7=-3; substitution verifies the equality."},"skills":["nonzero coefficient","inverse 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-20260924-equation-linear-solution-class-0001","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"743048b1e9caf0171fd58d132432a3c55f36ee61a8663c4b9f069ce4797cfb04","family_id":"qf-equation-linear-solution-class","seed":20261225,"semantic_template":"qf-equation-linear-solution-class/{\"a\":2,\"b\":0,\"c\":5,\"d\":-6,\"domain\":\"rationals\",\"form\":\"a*x+b=c*x+d\"}"},"fields":{"title":"Classifying a General Linear Equation","stem":"Over the rational numbers, classify the solution set of 2x+(0)=5x+(-6).","answer":{"kind":"short_text","value":"unique solution x=2","explanation":"(2−5)x=-6, so the equation has unique solution x=2."},"skills":["linear equations","solution classification"],"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-20260924-equation-linear-solution-class-0002","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7f404a7a4a382fcf74649d35f058c24f3cb3c3da4af39fb731dfb9dd87762d7d","family_id":"qf-equation-linear-solution-class","seed":20261226,"semantic_template":"qf-equation-linear-solution-class/{\"a\":2,\"b\":-3,\"c\":2,\"d\":-3,\"domain\":\"rationals\",\"form\":\"a*x+b=c*x+d\"}"},"fields":{"title":"Classifying a General Linear Equation","stem":"Over the rational numbers, classify the solution set of 2x+(-3)=2x+(-3).","answer":{"kind":"short_text","value":"infinitely many solutions","explanation":"Both sides reduce to the same expression, so every rational x is a solution."},"skills":["linear equations","solution classification"],"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-20260924-equation-linear-solution-class-0003","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"20046ad8b03f9e4a94bcd58d9bf9c4f8110bc47e9784d01c71464ea001b3c053","family_id":"qf-equation-linear-solution-class","seed":20261227,"semantic_template":"qf-equation-linear-solution-class/{\"a\":3,\"b\":2,\"c\":3,\"d\":3,\"domain\":\"rationals\",\"form\":\"a*x+b=c*x+d\"}"},"fields":{"title":"Classifying a General Linear Equation","stem":"Over the rational numbers, classify the solution set of 3x+(2)=3x+(3).","answer":{"kind":"short_text","value":"no solution","explanation":"The variable terms cancel but the constants disagree, so there is no solution."},"skills":["linear equations","solution classification"],"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-20260924-equation-linear-solution-class-0004","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a33abbe950528867ae2a479adcce9996bfba40ae840edc0dcfd461699fa275ea","family_id":"qf-equation-linear-solution-class","seed":20261228,"semantic_template":"qf-equation-linear-solution-class/{\"a\":5,\"b\":3,\"c\":8,\"d\":-3,\"domain\":\"rationals\",\"form\":\"a*x+b=c*x+d\"}"},"fields":{"title":"Classifying a General Linear Equation","stem":"Over the rational numbers, classify the solution set of 5x+(3)=8x+(-3).","answer":{"kind":"short_text","value":"unique solution x=2","explanation":"(5−8)x=-6, so the equation has unique solution x=2."},"skills":["linear equations","solution classification"],"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-20260924-equation-linear-solution-class-0005","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f5ca645d0de4538ea81c358decdeb015647245fb69f0ec95142feef92dd00da5","family_id":"qf-equation-linear-solution-class","seed":20261229,"semantic_template":"qf-equation-linear-solution-class/{\"a\":5,\"b\":0,\"c\":5,\"d\":0,\"domain\":\"rationals\",\"form\":\"a*x+b=c*x+d\"}"},"fields":{"title":"Classifying a General Linear Equation","stem":"Over the rational numbers, classify the solution set of 5x+(0)=5x+(0).","answer":{"kind":"short_text","value":"infinitely many solutions","explanation":"Both sides reduce to the same expression, so every rational x is a solution."},"skills":["linear equations","solution classification"],"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-20260924-equation-linear-solution-class-0006","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5cc98ee6ea82520b9fd550fe2ae993fa6233f1534b9722a6e11754032a4c6422","family_id":"qf-equation-linear-solution-class","seed":20261230,"semantic_template":"qf-equation-linear-solution-class/{\"a\":6,\"b\":5,\"c\":6,\"d\":6,\"domain\":\"rationals\",\"form\":\"a*x+b=c*x+d\"}"},"fields":{"title":"Classifying a General Linear Equation","stem":"Over the rational numbers, classify the solution set of 6x+(5)=6x+(6).","answer":{"kind":"short_text","value":"no solution","explanation":"The variable terms cancel but the constants disagree, so there is no solution."},"skills":["linear equations","solution classification"],"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-20260924-equation-linear-solution-class-0007","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"bde08f9650cca97fcf85a9f6c2dde9c7655f95623ce406eb1d48ba83e345a7a3","family_id":"qf-equation-linear-solution-class","seed":20261231,"semantic_template":"qf-equation-linear-solution-class/{\"a\":8,\"b\":6,\"c\":11,\"d\":0,\"domain\":\"rationals\",\"form\":\"a*x+b=c*x+d\"}"},"fields":{"title":"Classifying a General Linear Equation","stem":"Over the rational numbers, classify the solution set of 8x+(6)=11x+(0).","answer":{"kind":"short_text","value":"unique solution x=2","explanation":"(8−11)x=-6, so the equation has unique solution x=2."},"skills":["linear equations","solution classification"],"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-20260924-equation-linear-solution-class-0008","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"16acb8cf01b24bb64aa554af79cd48335630973de047e1527dc0746600e85c9c","family_id":"qf-equation-linear-solution-class","seed":20261232,"semantic_template":"qf-equation-linear-solution-class/{\"a\":8,\"b\":3,\"c\":8,\"d\":3,\"domain\":\"rationals\",\"form\":\"a*x+b=c*x+d\"}"},"fields":{"title":"Classifying a General Linear Equation","stem":"Over the rational numbers, classify the solution set of 8x+(3)=8x+(3).","answer":{"kind":"short_text","value":"infinitely many solutions","explanation":"Both sides reduce to the same expression, so every rational x is a solution."},"skills":["linear equations","solution classification"],"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-20260924-equation-linear-solution-class-0009","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"47fce281a147acd6c22049a0e1837702b9dc7f4c62a6fabdd108cc4fc68e705b","family_id":"qf-equation-linear-solution-class","seed":20261233,"semantic_template":"qf-equation-linear-solution-class/{\"a\":9,\"b\":8,\"c\":9,\"d\":9,\"domain\":\"rationals\",\"form\":\"a*x+b=c*x+d\"}"},"fields":{"title":"Classifying a General Linear Equation","stem":"Over the rational numbers, classify the solution set of 9x+(8)=9x+(9).","answer":{"kind":"short_text","value":"no solution","explanation":"The variable terms cancel but the constants disagree, so there is no solution."},"skills":["linear equations","solution classification"],"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-20260924-equation-linear-solution-class-0010","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d8de12d14101cc68b4fb409579838b1f82acb49f6275a200b1ec9c1da9204d03","family_id":"qf-equation-linear-solution-class","seed":20261234,"semantic_template":"qf-equation-linear-solution-class/{\"a\":11,\"b\":9,\"c\":14,\"d\":3,\"domain\":\"rationals\",\"form\":\"a*x+b=c*x+d\"}"},"fields":{"title":"Classifying a General Linear Equation","stem":"Over the rational numbers, classify the solution set of 11x+(9)=14x+(3).","answer":{"kind":"short_text","value":"unique solution x=2","explanation":"(11−14)x=-6, so the equation has unique solution x=2."},"skills":["linear equations","solution classification"],"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-20260924-equation-linear-solution-class-0011","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"47dc73d83d84821a44394c8f304d37602979661e10cee356361e680a4c5ade95","family_id":"qf-equation-linear-solution-class","seed":20261235,"semantic_template":"qf-equation-linear-solution-class/{\"a\":11,\"b\":6,\"c\":11,\"d\":6,\"domain\":\"rationals\",\"form\":\"a*x+b=c*x+d\"}"},"fields":{"title":"Classifying a General Linear Equation","stem":"Over the rational numbers, classify the solution set of 11x+(6)=11x+(6).","answer":{"kind":"short_text","value":"infinitely many solutions","explanation":"Both sides reduce to the same expression, so every rational x is a solution."},"skills":["linear equations","solution classification"],"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-20260924-equation-linear-solution-class-0012","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fa04cbed724f585759010ff76338dcf69e3af3fee48abcfe5b3c70a80339654c","family_id":"qf-equation-linear-solution-class","seed":20261236,"semantic_template":"qf-equation-linear-solution-class/{\"a\":12,\"b\":11,\"c\":12,\"d\":12,\"domain\":\"rationals\",\"form\":\"a*x+b=c*x+d\"}"},"fields":{"title":"Classifying a General Linear Equation","stem":"Over the rational numbers, classify the solution set of 12x+(11)=12x+(12).","answer":{"kind":"short_text","value":"no solution","explanation":"The variable terms cancel but the constants disagree, so there is no solution."},"skills":["linear equations","solution classification"],"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-20260924-equation-linear-solution-class-0013","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"807d8bba0230370b5d65f1d38c4eb84fef4497659c368139d8e46f78666bd7be","family_id":"qf-equation-linear-solution-class","seed":20261237,"semantic_template":"qf-equation-linear-solution-class/{\"a\":14,\"b\":12,\"c\":17,\"d\":6,\"domain\":\"rationals\",\"form\":\"a*x+b=c*x+d\"}"},"fields":{"title":"Classifying a General Linear Equation","stem":"Over the rational numbers, classify the solution set of 14x+(12)=17x+(6).","answer":{"kind":"short_text","value":"unique solution x=2","explanation":"(14−17)x=-6, so the equation has unique solution x=2."},"skills":["linear equations","solution classification"],"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-20260924-equation-linear-solution-class-0014","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f3b41e72f8208a59eb4e7f420e86f79a13b54cc1939854e7df1986ffdbbb73a9","family_id":"qf-equation-linear-solution-class","seed":20261238,"semantic_template":"qf-equation-linear-solution-class/{\"a\":14,\"b\":9,\"c\":14,\"d\":9,\"domain\":\"rationals\",\"form\":\"a*x+b=c*x+d\"}"},"fields":{"title":"Classifying a General Linear Equation","stem":"Over the rational numbers, classify the solution set of 14x+(9)=14x+(9).","answer":{"kind":"short_text","value":"infinitely many solutions","explanation":"Both sides reduce to the same expression, so every rational x is a solution."},"skills":["linear equations","solution classification"],"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-20260924-equation-linear-solution-class-0015","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ceb38778b4fc8b3216c30cb8a6ac43ee2f946e2b3d0925bc06b77e6d2896c46a","family_id":"qf-equation-linear-solution-class","seed":20261239,"semantic_template":"qf-equation-linear-solution-class/{\"a\":15,\"b\":14,\"c\":15,\"d\":15,\"domain\":\"rationals\",\"form\":\"a*x+b=c*x+d\"}"},"fields":{"title":"Classifying a General Linear Equation","stem":"Over the rational numbers, classify the solution set of 15x+(14)=15x+(15).","answer":{"kind":"short_text","value":"no solution","explanation":"The variable terms cancel but the constants disagree, so there is no solution."},"skills":["linear equations","solution classification"],"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-20260924-equation-linear-solution-class-0016","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"88928721090ec6b72412c6d8dc8211d6a9ca638dcb942337cc747be050cd0134","family_id":"qf-equation-linear-solution-class","seed":20261240,"semantic_template":"qf-equation-linear-solution-class/{\"a\":17,\"b\":15,\"c\":20,\"d\":9,\"domain\":\"rationals\",\"form\":\"a*x+b=c*x+d\"}"},"fields":{"title":"Classifying a General Linear Equation","stem":"Over the rational numbers, classify the solution set of 17x+(15)=20x+(9).","answer":{"kind":"short_text","value":"unique solution x=2","explanation":"(17−20)x=-6, so the equation has unique solution x=2."},"skills":["linear equations","solution classification"],"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-20260924-equation-linear-solution-class-0017","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"89fad7230f4682e3ab65dbd1e48484007f1853f76a038bf4d2232b3f7e403845","family_id":"qf-equation-linear-solution-class","seed":20261241,"semantic_template":"qf-equation-linear-solution-class/{\"a\":17,\"b\":12,\"c\":17,\"d\":12,\"domain\":\"rationals\",\"form\":\"a*x+b=c*x+d\"}"},"fields":{"title":"Classifying a General Linear Equation","stem":"Over the rational numbers, classify the solution set of 17x+(12)=17x+(12).","answer":{"kind":"short_text","value":"infinitely many solutions","explanation":"Both sides reduce to the same expression, so every rational x is a solution."},"skills":["linear equations","solution classification"],"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-20260924-equation-linear-solution-class-0018","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2ee6651ee347cdbe96ccd41ded7a9fa077a9af923ef414a16e10fd1af5ddb309","family_id":"qf-equation-linear-solution-class","seed":20261242,"semantic_template":"qf-equation-linear-solution-class/{\"a\":18,\"b\":17,\"c\":18,\"d\":18,\"domain\":\"rationals\",\"form\":\"a*x+b=c*x+d\"}"},"fields":{"title":"Classifying a General Linear Equation","stem":"Over the rational numbers, classify the solution set of 18x+(17)=18x+(18).","answer":{"kind":"short_text","value":"no solution","explanation":"The variable terms cancel but the constants disagree, so there is no solution."},"skills":["linear equations","solution classification"],"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-20260924-equation-linear-solution-class-0019","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"83077085f065e0bb88c4f675650ae223e31d4ac252223dbac0d279100f60e43c","family_id":"qf-equation-linear-solution-class","seed":20261243,"semantic_template":"qf-equation-linear-solution-class/{\"a\":20,\"b\":18,\"c\":23,\"d\":12,\"domain\":\"rationals\",\"form\":\"a*x+b=c*x+d\"}"},"fields":{"title":"Classifying a General Linear Equation","stem":"Over the rational numbers, classify the solution set of 20x+(18)=23x+(12).","answer":{"kind":"short_text","value":"unique solution x=2","explanation":"(20−23)x=-6, so the equation has unique solution x=2."},"skills":["linear equations","solution classification"],"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-20260924-equation-linear-solution-class-0020","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b181e5461da59101d72a956d0fa2eb9f8667cb1a88020ff16357ff4bdd19a477","family_id":"qf-equation-linear-solution-class","seed":20261244,"semantic_template":"qf-equation-linear-solution-class/{\"a\":20,\"b\":15,\"c\":20,\"d\":15,\"domain\":\"rationals\",\"form\":\"a*x+b=c*x+d\"}"},"fields":{"title":"Classifying a General Linear Equation","stem":"Over the rational numbers, classify the solution set of 20x+(15)=20x+(15).","answer":{"kind":"short_text","value":"infinitely many solutions","explanation":"Both sides reduce to the same expression, so every rational x is a solution."},"skills":["linear equations","solution classification"],"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-20260924-equation-linear-solution-class-0021","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"016937509547a5c9f2cacab1118f41c6a49cdfb80ea625dc235e009f8719ebca","family_id":"qf-equation-linear-solution-class","seed":20261245,"semantic_template":"qf-equation-linear-solution-class/{\"a\":21,\"b\":20,\"c\":21,\"d\":21,\"domain\":\"rationals\",\"form\":\"a*x+b=c*x+d\"}"},"fields":{"title":"Classifying a General Linear Equation","stem":"Over the rational numbers, classify the solution set of 21x+(20)=21x+(21).","answer":{"kind":"short_text","value":"no solution","explanation":"The variable terms cancel but the constants disagree, so there is no solution."},"skills":["linear equations","solution classification"],"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-20260924-equation-linear-solution-class-0022","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"eb4598c95854a21cc833040fff7d324ee0670608ae5814cb5be44619f9b105ba","family_id":"qf-equation-linear-solution-class","seed":20261246,"semantic_template":"qf-equation-linear-solution-class/{\"a\":23,\"b\":21,\"c\":26,\"d\":15,\"domain\":\"rationals\",\"form\":\"a*x+b=c*x+d\"}"},"fields":{"title":"Classifying a General Linear Equation","stem":"Over the rational numbers, classify the solution set of 23x+(21)=26x+(15).","answer":{"kind":"short_text","value":"unique solution x=2","explanation":"(23−26)x=-6, so the equation has unique solution x=2."},"skills":["linear equations","solution classification"],"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-20260924-equation-linear-solution-class-0023","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fa6d07b14502846b5453b8f3dfcaab50760352648865257329d624f487ad7ccb","family_id":"qf-equation-linear-solution-class","seed":20261247,"semantic_template":"qf-equation-linear-solution-class/{\"a\":23,\"b\":18,\"c\":23,\"d\":18,\"domain\":\"rationals\",\"form\":\"a*x+b=c*x+d\"}"},"fields":{"title":"Classifying a General Linear Equation","stem":"Over the rational numbers, classify the solution set of 23x+(18)=23x+(18).","answer":{"kind":"short_text","value":"infinitely many solutions","explanation":"Both sides reduce to the same expression, so every rational x is a solution."},"skills":["linear equations","solution classification"],"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-20260924-equation-linear-solution-class-0024","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1e443b6d4ee7476b9bac2fc053ce0f01c4486644999502876bace58daa1c913d","family_id":"qf-equation-linear-solution-class","seed":20261248,"semantic_template":"qf-equation-linear-solution-class/{\"a\":24,\"b\":23,\"c\":24,\"d\":24,\"domain\":\"rationals\",\"form\":\"a*x+b=c*x+d\"}"},"fields":{"title":"Classifying a General Linear Equation","stem":"Over the rational numbers, classify the solution set of 24x+(23)=24x+(24).","answer":{"kind":"short_text","value":"no solution","explanation":"The variable terms cancel but the constants disagree, so there is no solution."},"skills":["linear equations","solution classification"],"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-20260924-equation-linear-solution-class-0025","batch_id":"batch-20260924-equation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c03293b485afdbcf7658168bf92ca70e7e180d6c7c289e648a76e5f75cee8097","family_id":"qf-equation-linear-solution-class","seed":20261249,"semantic_template":"qf-equation-linear-solution-class/{\"a\":26,\"b\":24,\"c\":29,\"d\":18,\"domain\":\"rationals\",\"form\":\"a*x+b=c*x+d\"}"},"fields":{"title":"Classifying a General Linear Equation","stem":"Over the rational numbers, classify the solution set of 26x+(24)=29x+(18).","answer":{"kind":"short_text","value":"unique solution x=2","explanation":"(26−29)x=-6, so the equation has unique solution x=2."},"skills":["linear equations","solution classification"],"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."}}