1. 1.7 – Solve Absolute Value Equations and Inequalities Recall that the absolute value of a number x, written |x|, is the distance the number is from 0 on a number line. This understanding of absolute value can be extended to apply to simple absolute value equations.

2. 1.7 – Solve Absolute Value Equations and Inequalities

3. Example 1: Solve |x – 7| = 7

4. 1.7 – Solve Absolute Value Equations and Inequalities Example 1b: Solve |2x – 9| = 15

5. 1.7 – Solve Absolute Value Equations and Inequalities

6. Example 2: Solve |5x – 10| = 45

7. 1.7 – Solve Absolute Value Equations and Inequalities Example 2: Solve |4x + 10| = 28

8. 1.7 – Solve Absolute Value Equations and Inequalities Extraneous Solutions: When you solve an absolute value equation, it is possible for a solution to be extraneous. An extraneous solution is an apparent solution that must be rejected because it does not satisfy the original equation.

9. 1.7 – Solve Absolute Value Equations and Inequalities Example 3: Solve |2x + 12| = 4x

10. 1.7 – Solve Absolute Value Equations and Inequalities Example 3b: Solve |4x + 10| = 6x – 4

11. 1.7 – Solve Absolute Value Equations and Inequalities

12. Example 4: Solve |4x + 5| > 13

13. 1.7 – Solve Absolute Value Equations and Inequalities Example 4b: Solve |3x – 7| > 5