Solve the inequality.
`-9<\frac{2x+2}{4}-3\le7`
To solve the inequality, we can begin by isolating the variable.
Step 1: Simplify the expression inside the parentheses by combining like terms:
-9 < (2x + 2)/4 - 3 ≤ 7.
Simplify the fraction:
-9 < (2x + 2)/4 - 3 ≤ 7
-9 < (2x + 2)/4 - (3)(4)/4 ≤ 7
-9 < (2x + 2)/4 - 12/4 ≤ 7
-9 < (2x + 2)/4 - 3 ≤ 7
Simplify further:
-9 < (2x + 2)/4 - 3 ≤ 7
-9 < (2x + 2 - 3(4))/4 ≤ 7
-9 < (2x + 2 - 12)/4 ≤ 7
-9 < (2x - 10)/4 ≤ 7
Step 2: Multiply both sides of the inequality by 4 to remove the fraction:
-9*4 < (2x - 10)/4 * 4 ≤ 7*4
-36 < 2x - 10 ≤ 28
Step 3: Add 10 to all parts of the inequality to isolate the x variable:
-36 + 10 < 2x - 10 + 10 ≤ 28 + 10
-26 < 2x ≤ 38
Step 4: Divide both sides of the inequality by 2 to solve for x:
-26/2 < 2x/2 ≤ 38/2
-13 < x ≤ 19
Therefore, the solution to the inequality is -13 < x ≤ 19.