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?

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 didn't make any mistake

Answer 2

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

Explanation:

Marcie solved the following inequality

`-2(x -5) - 12 \leq  4 + 6(x + 3)`

-2 and 6 is distributed inside the parenthesis and did it correctly

`-2x + 10 - 12 \leq 4 + 6x + 18`

Like terms are combined and it is correct.

`-2x - 2 \leq  6x + 22`

Like terms are combined further

`-8x \leq 24`

When we divide or multiply an inequality by a negative number then we change the inequality sign.

`x \geq -3`

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