1. Copyright © 2010 Pearson Education, Inc. All rights reserved. 2.7 – Slide 1

2. Copyright © 2010 Pearson Education, Inc. All rights reserved. 2.7 – Slide 2 Equations, Inequalities, and Applications Chapter 2

3. Copyright © 2010 Pearson Education, Inc. All rights reserved. 2.7 – Slide 3 2.7 Solving Linear Inequalities

4. Copyright © 2010 Pearson Education, Inc. All rights reserved. 2.7 – Slide 4 2.7 Solving Linear Inequalities Objectives 1.Graph intervals on a number line. 2.Use the addition property of inequality. 3.Use the multiplication property of inequality. 4.Solve inequalities using both properties of inequality. 5.Solve linear inequalities with three parts. 6.Use inequalities to solve applied problems.

5. Copyright © 2010 Pearson Education, Inc. All rights reserved. 2.7 – Slide 5 Example 1 Graph x > –5. Graph Intervals on a Number Line 2.7 Solving Linear Inequalities The statement x > –5 says that x can represent any value greater than –5 but cannot equal –5. The interval is written (–5, ∞).

6. Copyright © 2010 Pearson Education, Inc. All rights reserved. 2.7 – Slide 6 Graph Intervals on a Number Line 2.7 Solving Linear Inequalities

7. Copyright © 2010 Pearson Education, Inc. All rights reserved. 2.7 – Slide 7 Example 2 Graph 3 > x. Graph Intervals on a Number Line 2.7 Solving Linear Inequalities The statement 3 > x means the same as x < 3. Interval notation: (–∞, 3).

8. Copyright © 2010 Pearson Education, Inc. All rights reserved. 2.7 – Slide 8 Example 3 Graph –3 < x < 2. Graph Intervals on a Number Line 2.7 Solving Linear Inequalities The statement –3 ≤ x < 2 is read “–3 is less than or equal to x and x is less than 2.” Interval notation: [–3, 2).

9. Copyright © 2010 Pearson Education, Inc. All rights reserved. 2.7 – Slide 9 Summary Graph Intervals on a Number Line 2.7 Solving Linear Inequalities

10. Copyright © 2010 Pearson Education, Inc. All rights reserved. 2.7 – Slide 10 Summary, continued Graph Intervals on a Number Line 2.7 Solving Linear Inequalities

11. Copyright © 2010 Pearson Education, Inc. All rights reserved. 2.7 – Slide 11 Use the Addition Property of Inequality 2.7 Solving Linear Inequalities

12. Copyright © 2010 Pearson Education, Inc. All rights reserved. 2.7 – Slide 12 Example 4 Solve 7 + 3k ≥ 2k – 5, and graph the solution set. Graph Intervals on a Number Line 2.7 Solving Linear Inequalities

13. Copyright © 2010 Pearson Education, Inc. All rights reserved. 2.7 – Slide 13 Use the Addition Property of Inequality 2.7 Solving Linear Inequalities (continued)

14. Copyright © 2010 Pearson Education, Inc. All rights reserved. 2.7 – Slide 14 Use the Addition Property of Inequality 2.7 Solving Linear Inequalities

15. Copyright © 2010 Pearson Education, Inc. All rights reserved. 2.7 – Slide 15 To see how the multiplication property of inequality words, consider the inequality 3 < 7. The Multiplication Property of Inequality 2.7 Solving Linear Inequalities (continued)

16. Copyright © 2010 Pearson Education, Inc. All rights reserved. 2.7 – Slide 16 To see how the multiplication property of inequality words, consider the inequality 3 < 7. The Multiplication Property of Inequality 2.7 Solving Linear Inequalities

17. Copyright © 2010 Pearson Education, Inc. All rights reserved. 2.7 – Slide 17 The Multiplication Property of Inequality 2.7 Solving Linear Inequalities

18. Copyright © 2010 Pearson Education, Inc. All rights reserved. 2.7 – Slide 18 The Multiplication Property of Inequality 2.7 Solving Linear Inequalities Example 6 Solve –4t ≥ 8, and graph the solution set. The solution set is (–∞, –2].

19. Copyright © 2010 Pearson Education, Inc. All rights reserved. 2.7 – Slide 19 Solve Inequalities Using both Properties of Inequality 2.7 Solving Linear Inequalities

20. Copyright © 2010 Pearson Education, Inc. All rights reserved. 2.7 – Slide 20 Solve Inequalities Using both Properties of Inequality 2.7 Solving Linear Inequalities Example 7 Solve 3x + 2 – 5 > x + 7 + 2x. Graph the solution set. (continued)

21. Copyright © 2010 Pearson Education, Inc. All rights reserved. 2.7 – Slide 21 Solve Inequalities Using both Properties of Inequality 2.7 Solving Linear Inequalities Example 7 Solve 3x + 2 – 5 > x + 7 + 2x. Graph the solution set. The solution set is (5, ∞).

22. Copyright © 2010 Pearson Education, Inc. All rights reserved. 2.7 – Slide 22 Solve Inequalities Using both Properties of Inequality 2.7 Solving Linear Inequalities Example 8 Solve 5(k – 3) – 7k ≥ 4(k – 3) + 9. Graph the solution set. (continued)

23. Copyright © 2010 Pearson Education, Inc. All rights reserved. 2.7 – Slide 23 Solve Inequalities Using both Properties of Inequality 2.7 Solving Linear Inequalities Example 8 Solve 5(k – 3) – 7k ≥ 4(k – 3) + 9. Graph the solution set. The solution set is (–∞, –2].

24. Copyright © 2010 Pearson Education, Inc. All rights reserved. 2.7 – Slide 24 Solve Linear Inequalities with Three Parts 2.7 Solving Linear Inequalities An inequality that says that one number is between two other numbers is a three-part inequality. The three-part inequality

25. Copyright © 2010 Pearson Education, Inc. All rights reserved. 2.7 – Slide 25 Solve Linear Inequalities with Three Parts 2.7 Solving Linear Inequalities

26. Copyright © 2010 Pearson Education, Inc. All rights reserved. 2.7 – Slide 26 Solve Linear Inequalities with Three Parts 2.7 Solving Linear Inequalities Example 10 Solve 4 ≤ 3x – 5 < 10. Graph the solution set. The solution set is [3, 5).

27. Copyright © 2010 Pearson Education, Inc. All rights reserved. 2.7 – Slide 27 Solve Linear Inequalities with Three Parts 2.7 Solving Linear Inequalities Summary of types of solutions:

28. Copyright © 2010 Pearson Education, Inc. All rights reserved. 2.7 – Slide 28 Use Inequalities to Solve Applied Problems 2.7 Solving Linear Inequalities Example 11 Finding an Average Test Score (continued)

29. Copyright © 2010 Pearson Education, Inc. All rights reserved. 2.7 – Slide 29 Use Inequalities to Solve Applied Problems 2.7 Solving Linear Inequalities Example 11 Finding an Average Test Score (continued)

30. Copyright © 2010 Pearson Education, Inc. All rights reserved. 2.7 – Slide 30 Use Inequalities to Solve Applied Problems 2.7 Solving Linear Inequalities Example 11 Finding an Average Test Score