To solve the compound inequality \( 13 > 2x - 3 > 5 \), we can break it down into two parts:

1. **First part**: \( 13 > 2x - 3 \)
2. **Second part**: \( 2x - 3 > 5 \)

### Solving the first part:
\[
13 > 2x - 3
\]
Add 3 to both sides:
\[
16 > 2x
\]
Divide by 2:
\[
8 > x \quad \text{or} \quad x < 8
\]

### Solving the second part:
\[
2x - 3 > 5
\]
Add 3 to both sides:
\[
2x > 8
\]
Divide by 2:
\[
x > 4
\]

### Combining the results:
So, we have:
\[
4 < x < 8
\]

### Final Solution:
The solution to the compound inequality is:
\[
x \in (4, 8)
\]

Would you like more details on any part of this solution? Here are some related questions you might consider:

1. How do you graph the solution \( (4, 8) \)?
2. What would happen if the inequality were \( 13 \geq 2x - 3 \)?
3. Can you explain how to solve a similar inequality step by step?
4. What are the applications of solving inequalities in real life?
5. How does solving inequalities differ from solving equations?

**Tip**: Always remember to treat the inequalities carefully, especially when multiplying or dividing by negative numbers, which reverses the inequality sign.

Explore the step-by-step solution to the compound inequality 13 > 2x - 3 > 5. This guide covers essential algebra concepts and shows how to derive the solution set (4, 8). Perfect for students in Grades 7-9.

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