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.

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.

anonymous · Answer

There isn't a mistake as far as I can see... Just imagine inequality signs as equal signs - they never change their position and don't really matter when you're solving the problem.

marigirl · Answer

−2(x − 5) − 12 ≤ 4 + 6(x + 3)     
−2x + 10 − 12 ≤ 4 + 6x + 18     Correct
−2x − 2 ≤ 6x + 22  simplified correctly
−8x ≤ 24  correct
x ≤ −3 * incorrect- when dividing both sides by a negative integer the sign will reverse -

marigirl · Answer

Whenever you multiply or divide an inequality by a negative number, you must flip the inequality sign.