Question

Solve the inequality.

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

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve this inequality, we can begin by isolating the expression `2x + 2`:

-9 < (2x + 2)/4 - 3 ≤ 7

To remove the fraction, we can multiply both sides of the inequality by 4:

4(-9) < 4[(2x + 2)/4 - 3] ≤ 4(7)
-36 < 2x + 2 - 12 ≤ 28

Next, we can simplify the inequality:

-36 - 2 < 2x + 2 - 2 ≤ 28 - 2
-38 < 2x < 26

Finally, we can divide by 2 on all three parts of the inequality:

-19 < x < 13

Therefore, the solution to the given inequality is -19 < x < 13.