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?

a. she subtracted 6x from both sides when she should have added 2x.
b. she added 2 to both sides when she should have subtracted 22.
c. when dividing by −8, she did not change the ≤ to ≥.
d. she did not make a mistake.

-2(x-5)-12≤4+6(x+3)
Use distributive property
-2(x)-2(-5)-12≤4+6(x)+6(3)
-2x+10-12≤4+6x+18
-2x-2≤6x+22
Add 2x to both side
-2x-2+2x≤6x+22+2x
-2≤8x+22
Subtract 22 to both side
-2-22≤8x+22-2
-24≤8x
Divided 8 to both side
-24/8≤8x/8
-3≤x
or
x≥-3
Um, there is another way to prove that there is one mistakes
-2(x-5)-12≤4+6(x+3)
-2x+10-12≤4+6x+18
-2x-2≤6x+22
-8x-2≤22
-8x≤24
x≥-3, so her mistakes is:
C. When dividing by −8, she did not change the ≤ to ≥. As a result, C is the final answer. Hope it help!