Question

Andrew solved the following inequality, and his work is shown below:

−4(x + 8) ≤ −2x + 50
−4x − 32 ≤ −2x + 50
−2x − 32 ≤ 50
−2x ≤ 82
x ≤ −41

What mistake did Andrew make in solving the inequality?

Answer 1

Below in bold.

Explanation:

−4(x + 8) ≤ −2x + 50

−4x − 32 ≤ −2x + 50 - correct

−2x − 32 ≤ 50 - correct

−2x ≤ 82 - correct

x ≤ −41 Error is on this line. When you divide by a negative ( here it is -2) you have to flip the inequality sign. The correct answer is x ≥ -41.