Warm-Up : Match the following graphs with its’ corresponding inequality:

1. Name:Date:Period: Topic: Solving & Graphing Compound InequalitiesEssential Question: How does a compound inequality differ from a regular inequality? What is the meaning of “and” and “or” in a compound inequality? Warm-Up: Match the following graphs with its’ corresponding inequality: • 5 > x a) • 5 < x • x > 10 • 5 ≥ x • 5 ≤ x • x < 10 - 10 - 5 0 5 10 b) - 10 - 5 0 5 10 c) - 10 0 10 - 5 5 d) 10 - 10 - 5 0 5 e) 10 - 10 - 5 0 5

2. Home-Learning Assignment #1 – Review:

3. Do you remember the difference between and and oron Set Theory? A B 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 B

4. Vocabulary: Compound Inequality A compound inequality consist of two inequalities connected by andoror.

5. Graphing Compound Inequalities

6. Guided Example: o o ● ● ● o 2 2 2 2 3 3 3 3 4 4 4 4 Graph x < 4 and x ≥ 2 a) Graph x < 4 b) Graph x ≥ 2 c) What if I Combine the graphs? d) Where do they intersect?

7. Guided Example: o o ● ● 2 2 2 2 3 3 3 3 4 4 4 4 Graph x < 2 or x ≥ 4 a) Graph x < 2 b) Graph x ≥ 4 c) Combine the graphs

8. o o -3 -2 -1 1) Which inequalities describe the following graph? • y > -3 or y < -1 • y > -3 and y < -1 • y ≤ -3 or y ≥ -1 • y ≥ -3 and y ≤ -1

9. o o 6 7 8 Lets graph the compound inequality 6 < m < 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.

10. 2) Which is equivalent to-3 < y < 5? • y > -3 or y < 5 • y > -3 and y < 5 • y < -3 or y > 5 • y < -3 and y > 5

11. 3) Which is equivalent to x > -5 and x ≤ 1? • -5 < x ≤ 1 • -5 > x ≥ 1 • -5 > x ≤ 1 • -5 < x ≥ 1

12. Writing Compound Inequalities

13. All real numbers that are greater than – 2 and less than 6 - 2 < x < 6 All real numbers that are less than 0 or greater than or equal to 5 x < 0 or x ≥ 5

14. Guided Example: All real numbers that are greater than zero and less than or equal to 4. All real numbers that are less than –1 or greater than 2

15. 4) Graph x < 2 or x ≥ 4 6) All real numbers that are greater than or equal to – 4 and less than 6 5) Graph x ≥ -1 or x ≤ 3 7) All real numbers that are less than or equal to 2.5 or greater than 6

16. 8) x is less than 4 and is at least -9

17. Solving & Graphing Compound Inequalities

18. Solving & Graphing and and 3 < 2m – 1 < 9 HINT: ONLY “AND” PROBLEMS WILL LOOK LIKE THIS. “OR” PROBLEMS MUST SAY “OR” and and

19. Answer: 3 < 2m – 1 < 9 + 1 + 1 + 1 ------------------------------ 4 < 2m < 10 2 2 2 2 < m < 5 - 5 0 5

21. Answer: – 8 – 8 3x > 9 3 3 x > 3 – 5 – 5 2x ≤ 2 2 2 x ≤ 1

22. 9) 10) 11) - 3 < - 1 – 2x ≤ 5 12) 13) 14) -15 ≤ –3x – 21 ≤ 25

23. Additional Practice: Page 204 - 206 (1 – 8, 14, 36) For those who complete the work before time is over, proceed to work on the following problems: Page 204 - 206 (10, 15, 24, 26, 38, 41, 55)

24. Based on the meaning of ‘and,’ why is this No Solution ? o o o o -6 -6 1 1 -3 -3 4 4 0 7 0 7 2x < -6 and 3x ≥ 12 ● Solve each inequality for x Graph each inequality Combine the graphs Where do they intersect? They do not! x cannot be greater than or equal to 4 and less than -3 No Solution!! ●

25. Wrap-Up:Vocabulary ReviewSummaryHome-Learning Assignment #2:Page 204 – 206 (9, 16, 18, 37, 54)