Question

Solve the inequality.

`-9<\frac{2x+2}{4}-3\le7`

Put your answer in the solution box below.

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve the inequality, we will work step by step:

Starting with the middle expression:
-9 < (2x+2)/4 - 3 ≤ 7

Add 3 to all parts of the inequality:
-9 + 3 < (2x+2)/4 - 3 + 3 ≤ 7 + 3
-6 < (2x+2)/4 ≤ 10

Multiply all parts of the inequality by 4 to get rid of the fraction:
(-6)*4 < [(2x+2)/4]*4 ≤ 10*4
-24 < 2x + 2 ≤ 40

Subtract 2 from all parts of the inequality:
-24 - 2 < 2x + 2 - 2 ≤ 40 - 2
-26 < 2x ≤ 38

Divide all parts of the inequality by 2:
-26/2 < 2x/2 ≤ 38/2
-13 < x ≤ 19

Therefore, the solution to the inequality is x ∈ (-13, 19].