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?
1.) He did not make a mistake.

2.) When dividing by −2, he did not change the direction of the sign.

3.) He added 2x to both sides when he should have subtracted.

4.) He added 32 to both sides when he should have subtracted.

Answer 1

2.) When dividing by −2, he did not change the direction of the sign.

Explanation:

-4(x + 8) ≤ -2x + 50 use the distributive property: a(b + c) = ab + ac

-4x - 32 ≤ -2x + 50 add 2x to both sides

-4x + 2x - 32 ≤ -2x + 2x + 50

-2x - 32 ≤ 50 add 32 to both sides

-2x - 32 + 32 ≤ +50 + 32

-2x ≤ 82 divide both sides by (-2) / flip the inequality sign/

x ≥ -41

Andrew's mistake:

2.) When dividing by −2, he did not change the direction of the sign.