https://file.aiquickdraw.com/mathbot/file/1729284432477m99wtafa.jpg

Let's analyze the number lines and form the appropriate compound inequalities.

### Problem 9:
- The graph shows two disjoint intervals: one from \(-5\) to \(-3\) and another from \(1\) to \(3\), both with open circles (indicating strict inequalities).
- Inequality: \( -5 < x < -3 \) or \( 1 < x < 3 \)

### Problem 10:
- This graph also shows two disjoint intervals. One from \(-5\) to \(-2\) and another from \(3\) to \(5\), both open at their endpoints.
- Inequality: \( -5 < x < -2 \) or \( 3 < x < 5 \)

### Problem 11:
- The interval is from \(-3\) to \(2\), and both endpoints are closed (indicated by solid dots), meaning the inequality includes the endpoints.
- Inequality: \( -3 \leq x \leq 2 \)

### Problem 12:
- The interval is from \(-5\) to \(1\), with the left endpoint \(-5\) closed (solid dot) and the right endpoint \(1\) open (open circle).
- Inequality: \( -5 \leq x < 1 \)

Would you like further clarification or details on any of these inequalities?

Here are 5 related questions:
1. What is the difference between open and closed intervals on a number line?
2. How do you express a compound inequality involving two disjoint intervals?
3. What types of problems use compound inequalities?
4. How do you solve compound inequalities involving absolute values?
5. Can compound inequalities represent all possible values for \(x\)?

**Tip:** When writing compound inequalities, "and" refers to values in the overlap, while "or" refers to values in either part.

Write a compound inequality for each solution set shown below (from a number line).

Learn how to write compound inequalities based on number line representations. This problem involves strict and inclusive intervals and helps students understand inequality notation using open and closed circles.

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