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Question 31544: Additive Equation

On this page
  1. Original question and givens
  2. Definition and scope
  3. Step-by-step derivation
  4. Reverse checks
  5. Result
  6. This question review and source binding

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R0062-31544 · q-20260924-equation-additive-solve-0019

Original question and givens

Solve x+(3)=2 over the integers.

  • G001 — Solve x+(3)=2 over the integers.

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.

Step-by-step derivation

S001 · implies

Before

source roles = [qf-equation-additive-solve, integers, no-operation-field, x+a=b]

After

derived = [[integer_solution_STRING]]

Conditions: none

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.

Step identifiers and dependencies

Rule: R62_EXACT_source_keys_domain_operation_form_AND_output_types · Uses: G001

S002 · implies

Before

source roles = [3, 2, x+a=b, integers]

After

derived = [Yes]

Conditions: none

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.

Step identifiers and dependencies

Rule: Equation_BASE_integer_coefficients_declared_Z_OR_Q_NOT_blanket_SAFE · Uses: G001, S001

S003 · calculation

Before

Equation additive ORIGINAL b minus a := sub(2, 3)

After

Equation additive ORIGINAL b minus a = -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.

Step identifiers and dependencies

Rule: exact_rational_arithmetic · Uses: G001, S002

S004 · calculation

Before

Equation additive reverse ORIGINAL solution plus a := sum(-1, 3)

After

Equation additive reverse ORIGINAL solution plus a = 2

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.

Step identifiers and dependencies

Rule: exact_rational_arithmetic · Uses: G001, S003

S005 · implies

Before

source roles = [3, 2]

After

derived = [-1, 2]

Conditions: none

Subtract the SAME a from both sides:x=b−a,still in Z.Add the ORIGINAL a back to verify ORIGINAL b.Return an integer string,not/1.

Step identifiers and dependencies

Rule: Equation_ADD_both_sides_subtract_same_a_Z_closed · Uses: G001, S004

Reverse checks

  • 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 additive reverse ORIGINAL solution plus a with exact rational arithmetic, not rounded decimals.
  • S003 · premise_and_result_audit — Recompute Equation additive ORIGINAL b minus 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

-1

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.

Source hashes and review receipts
  • input commit: 0f7be61e2c22317a4075561dc822c87d881a50db
  • original question SHA-256: bbafec664736ef17eb742552a77b1750db6d9cd6544d51c740682706e77c726c
  • candidate record SHA-256: e56a601e47d1cf9aec62a010850272afa621c387d2e59a22cb175b7465011d86
  • semantic review receipt SHA-256: 963099ffc9f754069fdce6792949a85ed350472465eaceb3038fa8011cf672bd
  • question-first witness SHA-256: d7655324c5d11528e1af90b757384cebd3313e19dc5f6f5b9b8ea7624fb06f6f
  • Lean: NOT_RUN · human review: NOT_PERFORMED
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