Find a−b when the linear equation is an identity in x.

01 / Standard#Your turn

3x-a=5-bx

Official paper · jm01-2026 · I.3 · PDF 2

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Infinitely many solutions require equality of both coefficients.

Hint 2

Match both the x coefficient and constant term.

Worked solution

Rearrange to a linear polynomial that vanishes for every real x.
$(3+b)x=a+5$
Both sides must have zero constant discrepancy and zero x coefficient.
$b=-3,\ a=-5,\quad a-b=-2$

C: −2.

Checks and common pitfalls: One solution and infinitely many solutions impose different conditions.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
Rearrange to a linear polynomial that vanishes for every real x.
$(3+b)x=a+5$
Both sides must have zero constant discrepancy and zero x coefficient.
$b=-3,\ a=-5,\quad a-b=-2$

Think first. Reveal a hint when the class is ready.

2026 JM01