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AlgebraVery hardEquivalent inequality

Algebra practice question

Which of the following inequalities has the same solution set as 4 − x ≥ 2x + 1?

  1. A. x ≤ 1Correct
  2. B. x ≥ 1
  3. C. x ≤ −1
  4. D. x ≤ 5/3

Answer: A. x ≤ 1

4 − x ≥ 2x + 1 gives 3 ≥ 3x, so x ≤ 1.

Why the other answers are wrong

B. x ≥ 1
The direction is reversed; no division by a negative occurred.
C. x ≤ −1
Sign error on the constant.
D. x ≤ 5/3
5/3 comes from 5 ≥ 3x, adding 1 instead of subtracting.

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