1. Solving Compound Inequalities

2. Domain: A-REI Reasoning with Equations & Inequalities Cluster: 1. Understand solving equations as a process of reasoning and explain the reasoning. Standard 1. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

3. Domain: A-REI Reasoning with Equations & Inequalities Cluster: 2. Solve equations and inequalities in one variable. Standard: 3. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

4. What is the difference between “and” and “ or” ? AND means intersection -only elements common to both sets are part of the solution. OR means union -Elements from both sets are part of the solution. A AB B

5. 1. Graph x < 4 and x ≥ 2 342 ● a) Graph x < 4 b) Graph x ≥ 2 342 o ● 342 o c) 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) Unite the graphs 342 o 342 ●

7. 3. Which inequalities describe the following graph? A. y > -3 or y < -1 B. y > -3 and y < -1 C. y ≤ -3 or y ≥ -1 D. y ≥ -3 and y ≤ -1 -2-3 o o Can also be written as: - 3 < y < -1

8. 4. Graph the compound inequality 6 < m < 8 786 o o “6 is less than m and m is less than 8” 6 78 6 78 o o “m is between 6 and 8”

9. 5. Which is equivalent to -3 < y < 5? A. y > -3 or y < 5 B. y > -3 and y < 5 C. y 5 D. y 5 05-3 o o

10. 6. Which is equivalent to x > -5 and x ≤ 1? A. -5 < x ≤ 1 B. -5 > x ≥ 1 C. -5 > x ≤ 1 D. -5 < x ≥ 1 o 0 1 -5

11. 7. Solve: 2x < -6 and 3x ≥ 12 1.Solve each inequality 1.Graph each solution 1.Where do they intersect? 1.They do not! No Solution !! -30-6 o -30-6 o 471 o ● 471 o ●

12. 8. Solve: 3x+2 < 2 or 1-x ≥ 4 05 -3 01 o -3-2-4 ● Unite the two sets o ●

13. 10. Graph x > -1 or x < 3 The entire number line is shaded!! What is the solution??? All Real Numbers 03

14. 10. Solve: 3 < 2m – 1 < 9 05 -5 See Next Slide for Different Method. Find the intersection of the two sets.

15. 10. Method 2: 05 -5