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

(B) when dividing by -5, he did not change the < to > 

Answer 2

For this case we observe that we have the following inequality:

-4 (x + 8) + 25 ≤ -2 + 1 (x - 50)

The first step is the distributive property on both sides of the inequality:

-4x - 32 + 25 ≤ -2 + 1x - 50

This step is written correctly.

The second step is to add similar terms:

-4x - 7 ≤ 1x - 52

This step is written correctly.

The third step is to pass the number 7 adding on the right side of the inequality:

-5x ≤ -45

This step is written correctly.

The last step is to divide between 5 both sides of the inequality. Then, multiply by -1. When multiplied by -1, the direction of the inequality changes:

x ≤9

This step is written incorrectly.

Answer:

Andrew did not change the symbol of the inequality in the last step.