3.2.3 Solving Compound Inequalities - Worksheet

Example 1:

1. An iguana needs to live in a warm environment. The temperature in a pet iguana’s cage should be between 70ºF and 95ºF inclusive. Write a compound inequality to show the temperatures that are within the recommended range. Graph the solutions.

Example 2: Solve each compound inequality and graph the solutions.

2. − 3 < x + 2 < 7

3. 5 ≤ 4 x + 1 ≤ 13

4. 2 < x + 2 < 5

5. 11 < 2 x + 3 < 21

Example 3:

Solve each compound inequality and graph the solutions.

6. x + 2 < − 6 OR x + 2 > 6

7. r − 1 < 0 OR r − 1 > 4

8. n + 2 < 3 OR n + 3 > 7

9. x − 1 < − 1 OR x − 5 > − 1

Example 4:

Write the compound inequality shown by each graph.

10.

11.

–6–5–4–3–2–1 0 1 2 3 4

–5–4–3–2–1 0 1 2 3 4 5

12.

13.

–10–8–6–4–2 0 2 4 6 8 10

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