16Hit1600
AlgebraVery hardInequality with a fraction and a negative

Algebra practice question

Which of the following describes all solutions to 5 − (x/3) ≥ 2?

  1. A. x ≤ 9Correct
  2. B. x ≥ 9
  3. C. x ≤ −9
  4. D. x ≥ 1

Answer: A. x ≤ 9

Subtract 5: −x/3 ≥ −3. Multiply by −3 and flip: x ≤ 9.

Why the other answers are wrong

B. x ≥ 9
x ≥ 9 forgets to flip when multiplying by a negative.
C. x ≤ −9
x ≤ −9 flips but gets the sign of 9 wrong.
D. x ≥ 1
x ≥ 1 comes from treating 5 − x/3 as (5 − x)/3 and dropping the flip.

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