Question

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

−4(x + 8) + 25 ≤ −2 + 1(x − 50)
−4x − 32 + 25 ≤ −2 + 1x − 50
−4x − 7 ≤ 1x − 52
−5x ≤ −45
x ≤ 9

What mistake did Andrew make in solving the inequality?

Answer 1

when he divided by -5 he was supposed to switch the inequality sign to the opposite direction.

Answer 2

The mistake is on the last line when he divided by -5 on both sides. When solving an inequality, we need to be careful with the direction of the inequality sign. We flip the inequality sign when we multiply or divide both sides of an inequality by a negative number.

This has to do with the way we order the numbers. 10 is greater than 5, but -10 is less than -5.