Solve 7×x=-21 over the integers; the coefficient 7 is explicitly nonzero.
G001 — Solve 7×x=-21 over the integers; the coefficient 7 is explicitly nonzero.
Definition and scope
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.
Check THIS bank interface:BASE equations use form/domain;BASE events/complement have no operation;factorials have no domain.ext18 uses local hyphens,other legacy operations underscores.Do not force every answer into a tuple or fraction.
The BASE bank checks integers,not an added SAFE limit.This candidate checks the frozen exact integer slice,not arbitrary unsafe JavaScript-number behavior.Distinguish solutions over Z and Q.
Equation multiplicative ORIGINAL b over nonzero a := div(-21, 7)
After
Equation multiplicative ORIGINAL b over nonzero a = -3
Conditions: none
Use ORIGINAL operands and declared order for exact integer/rational arithmetic,not floats.Bounds are family-specific:do not revalidate derived values as RAW inputs or add blanket SAFE/n64 caps to BASE families.
Equation multiplicative reverse ORIGINAL a times solution := mul(7, -3)
After
Equation multiplicative reverse ORIGINAL a times solution = -21
Conditions: none
Use ORIGINAL operands and declared order for exact integer/rational arithmetic,not floats.Bounds are family-specific:do not revalidate derived values as RAW inputs or add blanket SAFE/n64 caps to BASE families.
FIRST require a≠0 AND a divides b,then solve x=b/a IN Z.Negative a is legal.Nondivisibility fails this source family qualification;do not present a rational answer as an integer solution.
S005 · premise_and_result_audit — Reverse-check the ORIGINAL inputs,field roles,domain and premises.Consistency does not imply unique recovery of premises.Keep finite checking,independent review,formal proof and publication separate.
S004 · premise_and_result_audit — Recompute Equation multiplicative reverse ORIGINAL a times solution with exact rational arithmetic, not rounded decimals.
S003 · premise_and_result_audit — Recompute Equation multiplicative ORIGINAL b over nonzero a with exact rational arithmetic, not rounded decimals.
S002 · premise_and_result_audit — Reverse-check the ORIGINAL inputs,field roles,domain and premises.Consistency does not imply unique recovery of premises.Keep finite checking,independent review,formal proof and publication separate.
S001 · premise_and_result_audit — Reverse-check the ORIGINAL inputs,field roles,domain and premises.Consistency does not imply unique recovery of premises.Keep finite checking,independent review,formal proof and publication separate.
Result
-3
The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.
This question review and source binding
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.