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AlgebraEasyClearing a fraction in an inequality

Algebra practice question

Which of the following describes all solutions of x/4 ≥ 3?

  1. A. x ≥ 12Correct
  2. B. x ≤ 12
  3. C. x ≥ 3/4
  4. D. x ≥ 7

Answer: A. x ≥ 12

Multiply both sides by 4: x ≥ 12.

Why the other answers are wrong

B. x ≤ 12
Multiplying by the positive number 4 keeps the direction: x ≥ 12.
C. x ≥ 3/4
3/4 inverts the operation; multiply by 4 instead.
D. x ≥ 7
7 adds 4 and 3; the inequality multiplies: 4 · 3 = 12.

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