1. Holt McDougal Algebra 1 2-6 Solving Compound Inequalities Solve compound inequalities with one variable. Graph solution sets of compound inequalities with one variable. Objectives

2. Holt McDougal Algebra 1 2-6 Solving Compound Inequalities compound inequality intersection union Vocabulary

3. Holt McDougal Algebra 1 2-6 Solving Compound Inequalities The inequalities you have seen so far are simple inequalities. When two simple inequalities are combined into one statement by the words AND or OR, the result is called a compound inequality.

4. Holt McDougal Algebra 1 2-6 Solving Compound Inequalities

5. Holt McDougal Algebra 1 2-6 Solving Compound Inequalities You can graph the solutions of a compound inequality involving AND by using the idea of an overlapping region. The overlapping region is called the intersection and shows the numbers that are solutions of both inequalities.

6. Holt McDougal Algebra 1 2-6 Solving Compound Inequalities Example 2A: Solving Compound Inequalities Involving AND Solve the compound inequality and graph the solutions. –5 < x + 1 < 2 –1 – 1 – 1 –6 < x < 1 –10 –8 –6–4 –2 0246810

7. Holt McDougal Algebra 1 2-6 Solving Compound Inequalities Example 2B: Solving Compound Inequalities Involving AND Solve the compound inequality and graph the solutions. 8 < 3x – 1 ≤ 11 +1 +1 +1 9 < 3x ≤ 12 3 < x ≤ 4

8. Holt McDougal Algebra 1 2-6 Solving Compound Inequalities Solve the compound inequality and graph the solutions. Check It Out! Example 2a –9 < x – 10 < –5 +10 +10 +10 –9 < x – 10 < –5 1 < x < 5 –5 –4 –3–2 –1 012345

9. Holt McDougal Algebra 1 2-6 Solving Compound Inequalities Solve the compound inequality and graph the solutions. Check It Out! Example 2b –4 ≤ 3n + 5 < 11 –5 – 5 – 5 –9 ≤ 3n < 6 –3 ≤ n < 2 –5 –4 –3–2 –1 012345

10. Holt McDougal Algebra 1 2-6 Solving Compound Inequalities Example 3A: Solving Compound Inequalities Involving OR Solve the inequality and graph the solutions. 8 + t ≥ 7 OR 8 + t < 2 –8 –8 –8 −8 t ≥ –1 OR t < –6 –10 –8 –6–4 –2 0246810

11. Holt McDougal Algebra 1 2-6 Solving Compound Inequalities Example 3B: Solving Compound Inequalities Involving OR Solve the inequality and graph the solutions. 4x ≤ 20 OR 3x > 21 x ≤ 5 OR x > 7 0246810 –10 –8 –6–4 –2

12. Holt McDougal Algebra 1 2-6 Solving Compound Inequalities Solve the compound inequality and graph the solutions. Check It Out! Example 3a 2 +r 19 –2 –2 –5 –5 r 14 –4 –2 02 4 6810121416

13. Holt McDougal Algebra 1 2-6 Solving Compound Inequalities Solve the compound inequality and graph the solutions. Check It Out! Example 3b 7x ≥ 21 OR 2x < –2 x ≥ 3 OR x < –1 –5 –4 –3–2 –1 012345

14. Holt McDougal Algebra 1 2-6 Solving Compound Inequalities Lesson Quiz: Part I 1. The target heart rate during exercise for a 15 year-old is between 154 and 174 beats per minute inclusive. Write a compound inequality to show the heart rates that are within the target range. Graph the solutions. 154 ≤ h ≤ 174

15. Holt McDougal Algebra 1 2-6 Solving Compound Inequalities Lesson Quiz: Part II Solve each compound inequality and graph the solutions. 2. 2 ≤ 2w + 4 ≤ 12 –1 ≤ w ≤ 4 3. 3 + r > −2 OR 3 + r < −7 r > –5 OR r < –10

16. Holt McDougal Algebra 1 2-6 Solving Compound Inequalities Lesson Quiz: Part III Write the compound inequality shown by each graph. 4. x < −7 OR x ≥ 0 5. −2 ≤ a < 4