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?

This is what she did:

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

The mistake is in the last step.
she divided by -8 and she didn't chage the sign of inequality.
When you multiply or divide by a negative number the sign of the inequality has to be changed.

The right step would show:
x ≥ -3

Looks pretty good to me!