1. Warm Up Use the numbers: -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 to answer the following questions. 1.What numbers are less than or equal to –1 AND greater than or equal to –2? 2.Which numbers are greater than 1 OR less than –3? 3.Which numbers are less than or equal to –2 AND less than or equal to 2? 4.Which numbers are greater than –1 OR greater than 3?

2. Warm Up Answers Use the numbers: -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 to answer the following questions. 1.What numbers are less than or equal to –1 AND greater than or equal to –2? –2, -1 2.Which numbers are greater than 1 OR less than –3? -5, -4, 2, 3, 4, 5 3.Which numbers are less than or equal to –2 AND less than or equal to 2? –5, -4, -3, -2 4.Which numbers are greater than –1 OR greater than 3? 0, 1, 2, 3, 4, 5

3. Objectives The student will be able to: 1. solve compound inequalities. 2. graph the solution sets of compound inequalities. Designed by Skip Tyler, Varina High School Modified by Lisa Hoffmann Troy Buchanan High School

4. What is the difference between and and or ? AND means intersection -what do the two items have in common? OR means union -if it is in one item, it is in the solution A AB B

5. 1) Graph x < 4 and x ≥ 2 342 ● a) Graph x < 4 b) Graph x ≥ 2 342 o c) Combine the graphs ● 342 o d) Where do they intersect? ● 342 o

6. 2) Graph x < 2 or x ≥ 4 342 ● a) Graph x < 2 b) Graph x ≥ 4 342 o c) Combine the graphs 342 o 342 ● 342 ● o

7. 3) Which inequalities describe the following graph? -2-3 o o Answer Now 1.y > -3 or y < -1 2.y > -3 and y < -1 3.y ≤ -3 or y ≥ -1 4.y ≥ -3 and y ≤ -1 This is also: -3 < y < -1

8. When written this way, it is the same thing as 6 < m AND m < 8 It can be rewritten as m > 6 and m < 8 and graphed as previously shown, however, it is easier to graph everything between 6 and 8! 4) Graph the compound inequality 6 < m < 8 786 o o

9. 5) Which is equivalent to -3 < y < 5? 1.y > -3 or y < 5 2.y > -3 and y < 5 3.y 5 4.y 5 Answer Now

10. 6) Which is equivalent to x > -5 and x ≤ 1? 1.-5 < x ≤ 1 2.-5 > x ≥ 1 3.-5 > x ≤ 1 4.-5 < x ≥ 1 Answer Now

11. 7) 2x < -6 and 3x ≥ 12 1.Solve each inequality for x 2.Graph each inequality 3.Combine the graphs 4.Where do they intersect? 5.They do not! x cannot be greater than or equal to 4 and less than -3 No Solution!! -30-6 o 471 o 471 o -30-6 o

12. 8) Graph 3 < 2m + 1 < 9 Remember, when written like this, it is an AND problem! 3 < 2m + 1 AND 2m + 1 < 9 Solve each inequality. Graph the intersection of 1 < m and m < 4. 241 o o

13. 8) Graph 3 < 2m + 1 < 9 Another Way: Solve for m in the middle 3 < 2m + 1 < 9 -1 -1 -1 241 o o 2 < 2m < 8 1 < m < 4

14. 9) Graph x < 2 or x ≥ 4 05 -5

15. 10) Graph x ≥ -1 or x ≤ 3 The whole line is shaded!!