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R0008-04776 · q-20261008-advance-20261011-r03-variable-expression-0001
All operations and evaluations are exact in Q, not truncated natural-number arithmetic. E(x)=(0)x+(-3) is an expression, not an equation. Ordered x environments=[0/3, -1/2]. Give the two E values. Use exact reduced fractions with positive denominators, retaining /1 for integers.
G001 — All operations and evaluations are exact in Q, not truncated natural-number arithmetic. E(x)=(0)x+(-3) is an expression, not an equation. Ordered x environments=[0/3, -1/2]. Give the two E values. Use exact reduced fractions with positive denominators, retaining /1 for integers.Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate.
Before
typed rational expression and explicitly given environment
After
evaluation,not solving an equation
Conditions: none
Evaluating an expression is not solving an equation;substitute only the supplied environment without inventing roots or changing bindings.
Rule: expression_environment_scope · Uses: G001
Before
environment0 ax := mul(0, 0)
After
environment0 ax = 0
Conditions: none
Substitute this environment's x into the product term.
Rule: exact_rational_arithmetic · Uses: G001, S001
Before
environment0 ax+b := sum(0, -3)
After
environment0 ax+b = -3
Conditions: none
Then add b from the same expression.
Rule: exact_rational_arithmetic · Uses: G001, S002
Before
environment1 ax := mul(0, -1/2)
After
environment1 ax = 0
Conditions: none
Substitute this environment's x into the product term.
Rule: exact_rational_arithmetic · Uses: G001, S003
Before
environment1 ax+b := sum(0, -3)
After
environment1 ax+b = -3
Conditions: none
Then add b from the same expression.
Rule: exact_rational_arithmetic · Uses: G001, S004
Before
[-3/1, -3/1]
After
ordered independent evaluations of the same expression
Conditions: none
Read both environments from the original data;the second evaluation does not inherit a mutated first substitution.When a=0 the constant expression is independent of x.
Rule: separate_expression_environments · Uses: G001, S005
S006 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S005 · premise_and_result_audit — Recompute environment1 ax+b with exact rational arithmetic, not rounded decimals.S004 · premise_and_result_audit — Recompute environment1 ax with exact rational arithmetic, not rounded decimals.S003 · premise_and_result_audit — Recompute environment0 ax+b with exact rational arithmetic, not rounded decimals.S002 · premise_and_result_audit — Recompute environment0 ax with exact rational arithmetic, not rounded decimals.S001 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.(-3/1, -3/1)
The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.
Review date: 2026-10-26
Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof.
input commit: 0f7be61e2c22317a4075561dc822c87d881a50dboriginal question SHA-256: eac2e4d58b94837a6dddb257f787bfba15f29063065f6c8c1a45f4e67fd8e365candidate record SHA-256: 6f653d02e6912e8aa8c25c561652c8c3fd08073a278fcd06ff939906bc92618asemantic review receipt SHA-256: b6e05a3e8193a93db505dbf337528fca72e2e41528b1e92b698a3f0683d74289question-first witness SHA-256: caa8693baf0b91acd09a20215d1aa6954ae513fc0b0814f26ac1c8c834b60d67Lean: NOT_RUN · human review: NOT_PERFORMED