Question 6658: Original Rational Equation Sides and Defect

Original question and givens

Use the original equation’s common rational domain. L(x)=((-5)x+(8))/(-2), R(x)=(0)x+(-7), q≠0, x=8/2. Give (L, R, L−R, does the original equation hold?). Use exact reduced fractions with positive denominators, retaining /1 for integers.

• G001 — Use the original equation’s common rational domain. L(x)=((-5)x+(8))/(-2), R(x)=(0)x+(-7), q≠0, x=8/2. Give (L, R, L−R, does the original equation hold?). Use exact reduced fractions with positive denominators, retaining /1 for 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.

• mko-equation

Step-by-step derivation

common rational domain with original equation definitions

evaluate/classify the given model without enlarging its original domain

original left numerator linear product := mul(-5, 4)

original left numerator linear product = -20

original left numerator affine value := sum(-20, 8)

original left numerator affine value = -12

original right linear product := mul(0, 4)

original right linear product = 0

original right affine value := sum(0, -7)

original right affine value = -7

original left quotient := div(-12, -2)

original left quotient = 6

original two-side residual := sub(6, -7)

original two-side residual = 13

q=-2≠0;x=4/1;L−R=13

original equation at this x=No

Reverse checks

• S008 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S007 · premise_and_result_audit — Recompute original two-side residual with exact rational arithmetic, not rounded decimals.
• S006 · premise_and_result_audit — Recompute original left quotient with exact rational arithmetic, not rounded decimals.
• S005 · premise_and_result_audit — Recompute original right affine value with exact rational arithmetic, not rounded decimals.
• S004 · premise_and_result_audit — Recompute original right linear product with exact rational arithmetic, not rounded decimals.
• S003 · premise_and_result_audit — Recompute original left numerator affine value with exact rational arithmetic, not rounded decimals.
• S002 · premise_and_result_audit — Recompute original left numerator linear product 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.

Result

(6/1, -7/1, 13/1, 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.