1. WARM UPS 1/15 #1 Solve and graph the compound inequality –5 ≤ x – 1 ≤ 2 #2 Put the answer to #1 in set-builder notation. #3 Solve and graph the inequality 5(x+2) > 25

4. CHAPTER 5.5 Solving Absolute Value Inequalities

5. Case 1 Remove the absolute value symbols. Keep everything else the same! Case 2 Remove the absolute value symbols. Flip the inequality symbol. Change the sign (positive or negative) of the answer. SOLVING ABSOLUTE VALUE INEQUALITIES FIRST: Make two cases, and solve each individually… SECOND: Graph both solutions on the same number line.

6. x – 3 < 12 x – 3 > -12 Case 1Case 2 EXAMPLE #1 X – 3 < 12

7. X + 4 < 6 X + 4 > -6 Case 1Case 2 EXAMPLE #2 X + 4 < 6

8. Case 1Case 2 EXAMPLE #3 X + 6 < -8

10. EXAMPLE #4 RAINFALL The average annual rainfall in California for the last 100 years is 23 inches. However, the annual rainfall can differ by 10 inches from the 100 year average. What is the range of annual rainfall for California?

11. Case 1Case 2 EXAMPLE #4 RAINFALL X – 23 < 10 X – 23 > -10

12. Case 1Case 2 EXAMPLE #5 3X – 3 > 9

13. Case 1Case 2 EXAMPLE #6 2X + 7 > -11