Question

Keesha is having trouble solving the following compound inequality. She arrived at a final answer (below), but when she checked her work, she discovered that it is incorrect! Find Keesha’s error and explain to her how to fix it and solve the problem correctly. Then, provide the correct answer.

14 < 2x + 12 ≤ 24
-14 – 12 < 2x + 12 – 12 ≤ 24
2 < 2x ≤ 24
2/2 < 2x/2 ≤ 24/2
1 < x ≤ 12

Above is Keesha's answer, which I'm trying to find the error in and solve it correctly, but I don't understand, so if someone could please explain how to find the answer, it would be greatly appreciated.

Answer 1

where did that -14 in step 2 come from?
And the 12 should have been subtracted from all three quantities.
It should have been
14 - 12 < 2x + 12 - 12 ≤ 24 - 12
2 < 2x ≤ 12
1 < x ≤ 6

Answer 2

Thank you so much!

Answer 3

The RIGHT answer is: -12 should of been added to all three quantities.
14 + -12 < 2x +12 + -12 <_ 24 + -12
2 < 2x <_ 12
2/2 < 2x/2 <_ 12/2
1 < x <_ 6