Question 6664: Original Rational Equation Sides and Defect

Original question and givens

Use the original equation’s common rational domain. L(x)=((1)x+(14))/(-2), R(x)=(0)x+(-13), q≠0, x=14/2. 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)=((1)x+(14))/(-2), R(x)=(0)x+(-13), q≠0, x=14/2. 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(1, 7)

original left numerator linear product = 7

original left numerator affine value := sum(7, 14)

original left numerator affine value = 21

original right linear product := mul(0, 7)

original right linear product = 0

original right affine value := sum(0, -13)

original right affine value = -13

original left quotient := div(21, -2)

original left quotient = -21/2

original two-side residual := sub(-21/2, -13)

original two-side residual = 5/2

q=-2≠0;x=7/1;L−R=5/2

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

(-21/2, -13/1, 5/2, 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.