Let's solve the inequality \(-3 < \frac{3}{2}(2 - x) \leq 5\).

### Step 1: Break it into two separate inequalities
1. \(-3 < \frac{3}{2}(2 - x)\)
2. \(\frac{3}{2}(2 - x) \leq 5\)

### Step 2: Solve each inequality

#### Inequality 1: \(-3 < \frac{3}{2}(2 - x)\)
1. Multiply both sides by \(\frac{2}{3}\):
   \[
   -2 < 2 - x
   \]
2. Subtract 2 from both sides:
   \[
   -4 < -x
   \]
3. Multiply by \(-1\) and reverse the inequality sign:
   \[
   x < 4
   \]

#### Inequality 2: \(\frac{3}{2}(2 - x) \leq 5\)
1. Multiply both sides by \(\frac{2}{3}\):
   \[
   2 - x

Learn how to solve the inequality -3 < (3/2)(2 - x) <= 5 step-by-step. This problem involves inequalities and requires multiplication and division operations. Suitable for high school students (Grades 9-12).

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