1. Solving Compound Inequalities

2. Objective Today you will solve compound inequalities containing the word and, and graph their solution set. Today you will solve compound inequalities containing the word or, and graph their solution set.

3. WHY?!... Real world!! To ride the Mind Eraser roller coaster at Six Flags in Baltimore, Maryland, you must be at least 52 inches tall, and your height cannot exceed 72 inches. If h represents the height of a rider, we can write two inequalities to represent this. At least 52 inches h ≥ 52 Cannot exceed 72 inches h ≤ 72 Ssooooo, 52 ≤ h ≤ 72

4. Inequalities Containing AND When considered together, two inequalities such as h ≥ 52 and h ≤ 72 form a compound inequality. A compound inequality containing and is only true if both inequalities are true. Its graph is where the graphs of the two inequalities overlap. This is called the intersection of the two graphs.

5. The intersection can be found by graphing each inequality and then determining where the graphs intersect. x ≥ 3 x < 7 (graph on the board!) x ≥ 3 and x < 7 3 ≤ x < 7

6. Solve and Graph an Intersection Solve -2 ≤ x – 3 < 4 using and. Then solve each inequality. (First, express -2 ≤ x – 3 < 4 using and. Then solve!) -2 ≤ x – 3 x – 3 < 4 1 ≤ xx < 7 GRAPH BOTH OF THESE (on the board)

7. YOUR TURN! Solve each compound inequality. Then graph the solution set. 1)y – 3 ≥ -11 and y – 3 ≤ -8 2)6 ≤ r + 7 < 10

8. Inequalities Containing OR Another type of compound inequality contains the word or. A compound inequality containing or is true if at least one of the inequalities is true. Its graph is the union of the graphs of two inequalities. On board: x > 2 or x ≤ -1

9. Solve and Graph a Union Solve -2m + 7 ≤ 13 or 5m + 12 > 37. Then graph the solution set. -2m + 7 ≤ 13 -2m ≤ 6 m ≥ -3 5m + 12 > 37 5m > 25 m > 5 GRAPH ON THE BOARD!

10. YOUR TURN! a + 1 < 4 or a – 1 ≥ 3