Question

Marcie solved the following inequality, and her work is shown below:

−2(x − 5) − 12 ≤ 4 + 6(x + 3)
−2x + 10 − 12 ≤ 4 + 6x + 18
−2x − 2 ≤ 6x + 22
−8x ≤ 24
x ≤ −3

What mistake did Marcie make in solving the inequality? (2 points)


She subtracted 6x from both sides when she should have added 2x.

She added 2 to both sides when she should have subtracted 22.

When dividing by −8, she did not change the ≤ to ≥.

She did not make a mistake.

Answer 1

She forgot to flip the inequality when dividing by a negative

Explanation:

−2(x − 5) − 12 ≤ 4 + 6(x + 3)

Distribute the -2 and the 6

-2x+10 -12 ≤ 4 + 6x + 18

Combine like terms

-2x-2 ≤ 6x+22

Subtract 6x from each side

-2x-6x-2 ≤ 6x-6x+22

-8x-2 ≤ +22

Add 2 to each side

-8x-2+2 ≤ +22+2

−8x ≤ 24

Divide by -3. Remember when multiplying or dividing by a negative to flip the inequality

-8x/-8 ≥ 24/-8

x≥-3