Over the integers, consider x+(12)=-1 with candidate x=-12. After substitution into the original equation, is the candidate a solution?
G001 — Over the integers, consider x+(12)=-1 with candidate x=-12. After substitution into the original equation, is the candidate a solution?
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 candidate ORIGINAL x plus a := sum(-12, 12)
After
Equation candidate ORIGINAL x plus a = 0
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 candidate ORIGINAL left minus right := sub(0, -1)
After
Equation candidate ORIGINAL left minus right = 1
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.
Substitute the ORIGINAL candidate in x+a=b;it is a solution ONLY when both sides agree.No rejects THIS candidate,not all equation solutions,and is not a nearness test.
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 candidate ORIGINAL left minus right with exact rational arithmetic, not rounded decimals.
S003 · premise_and_result_audit — Recompute Equation candidate ORIGINAL x plus 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
No
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.