1. Chapter 1 Section 1.7

2. Yesterday’s Exit Slip -2

3. Objectives: O To solve compound inequalities using and and or. O To solve inequalities involving absolute value and graph the solutions. Why do we need this? You can use absolute value inequalities to solve problems involving entertainment and education.

4. Compound Inequalities A compound inequality is an equation with two or more inequalities joined together with either "and" or "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 A B B

5. Example Graph x < 4 and x ≥ 2 a) Graph x < 4 b) Graph x ≥ 2 c) Combine the graphs d) Where do they intersect? 3 4 2 o 3 4 2 ● ● 3 4 2 o

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

7. Example Solve and Graph: 9 < 3x + 6 < 15 9 < 3x + 6 < 15 9 < 3x + 6 3x + 6 < 15 1 < x x < 3 013 1< x < 3

8. Solving Absolute Value Inequality Why do you think we need to review compound inequalities before continuing with absolute value inequalities?

9. Example Solve and Graph: |2x + 4|  12 |2x + 4|  12 2x + 4  122x + 4  -12 2x  8 x  4 2x  -16 x  -8 0 4 -8 great OR or

10. Example Solve and Graph: |x - 3| < 2 |x - 3| < 2 x -3 < 2x – 3 > -2 x < 5 x > -2 0 5 -2 less th and and

11. Writing Absolute Value Inequalities You work in the quality control department of a manufacturing company. The diameter of a drill bit must be between 0.62 inch and 0.63 inch. Write an absolute-value inequality to represent this requirement. How do we solve this?

12. Solution Let d represent the diameter (in inches) of the drill bit. O Write a compound inequality. O Find the halfway point. O Subtract 0.625 from each part of the compound inequality. O Rewrite as an absolute-value inequality. 0.62 ≤ d ≤ 0.63 0.625 0.62 - 0.625 ≤ d - 0.625 ≤ 0.63 - 0.625 -0.005 ≤ d - 0.625 ≤ 0.005 |d - 0.625|≤ 0.005

13. Mid-Exit tickets These were our objectives: O To solve compound inequalities using and and or. O To solve inequalities involving absolute value and graph the solutions. Keep these in mind while answering your questions.