1. Slide 2- 1 Copyright © 2012 Pearson Education, Inc. Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

2. Copyright © 2012 Pearson Education, Inc. 2.1Linear Functions and Models 2.2Equations of Lines 2.3Linear Equations 2.4Linear Inequalities 2.5 Absolute Value Equations and Inequalities Linear Functions and Equations 2

3. Copyright © 2012 Pearson Education, Inc. Absolute Value Equations and Inequalities ♦ Evaluate and graph the absolute value function ♦ Solve absolute value equations ♦ Solve absolute value inequalities 2.5

4. Slide 2- 4 Copyright © 2012 Pearson Education, Inc. Absolute Value Function The symbol for the absolute value of x is

5. Slide 2- 5 Copyright © 2012 Pearson Education, Inc. Solving Absolute Value Equations

6. Slide 2- 6 Copyright © 2012 Pearson Education, Inc. Example Solve Solution The solutions are ‒ 1 and 2.

7. Slide 2- 7 Copyright © 2012 Pearson Education, Inc. Example Solve Solution The solutions are ‒ 1 and 1.

8. Slide 2- 8 Copyright © 2012 Pearson Education, Inc. Solving Absolute Value Inequalities

9. Slide 2- 9 Copyright © 2012 Pearson Education, Inc. Example Solve │1  2x │ > 3. Solution From a previous example the solutions of the equation │1  2x │ = 3 are  1 and 2. Thus the solutions for the inequality │1  2x │ > 3 are x 2. In interval notation this is (  ∞,  1) U (2, ∞).

10. Slide 2- 10 Copyright © 2012 Pearson Education, Inc. Example Solve │1  2x │ ≤ 3. Solution From an earlier example the solutions of the equation │1  2x │= 3 are  1 and 2. Thus the solutions for the inequality│1  2x │ ≤ 3 are  1 ≤ x ≤ 2. In interval notation this is [  1, 2].