1. Drill # 10 Solve the absolute value equation: 1. 3 | 2x – 2 | + 2 = 3x + 8 Solve each inequality and graph the solution. 2. 3 – (x – 1) > 2 ( x + 2 ) 3. 6 – 4x < x – 3

2. Drill # 11 Solve the absolute value equation: 1. 3|2x + 2| – 2x = x + 3 Solve each inequality and graph the solution.

3. Drill #12 1. -2 | x – 1| + 3 = 2x + 1 Solve each compound inequality and graph the solution: 2.x + 6 < 5x + 2 < 17 3.3x + 6 > -2(x – 2) and x – 5 < 3x + 7 4.2x + 7 > 11 or -2x + 2 > 6

4. Drill #13 Solve each compound inequality and graph the solution: 1.3x + 2 < 5x – 6 < 6(x – 2) 2.|3x – 4| > 10 3.-½|-3n – 9| < 6 4. 3|2y – 4| – 6 < 12

5. Drill #14 Solve each compound inequality and graph the solution: 1.3x < 6x – 6 < 4(x – 2) 2.-|3x – 4| +7 < 10 3.|-3n – 9|+10 < 6 4. 3|2y – 5| – 10 < 11

6. 1-6 Solving Compound and Absolute Value Inequalities Objective: To solve inequalities using and and or, and to solve inequalities involving absolute value and graph the solution.

7. Compound Inequalities* Compound Inequality: An inequality containing and or or. NOTE: To solve a compound inequality you must solve each part.

8. Intersections* Intersection: The graph of a compound containing and. Only true if both parts are true. The graph of a compound inequality containing and is the intersection of the graph of the 2 inequalities, or where their graphs overlap. Examples: Ex1:x + 3 > 5 and 3x – 5 < 2 EX2:8 < 3y – 7 < 23

9. Solutions to intersections The solution sets to intersections should be written with set-builder notation with a single compound inequality: Lower bound < x < upperbound { x | 1 < x < 3 } NOTE:The graphs of intersections are usually segments.

10. Unions * Union: The graph of a compound inequality containing or. True if either part of the inequality is true. The graph of a compound inequality containing or is the union of the graph of the 2 inequalities. Examples: Ex1:x – 2 > 1 or x + 5 > 15 Ex2:5j > 15 or -3j > 21

11. Solutions to unions* The solution sets to unions should be written with set-builder notation with a two inequalities separated by or: { x | x > 4 or x < -1 } The graphs of intersections are generally a disjunction, two separate graphs going in opposite directions.

12. Intersections* x < 3 and x < 5 x > 3 and x > 5 x > 3 and x < 5 x 5

13. All possible Unions* x < 3 or x < 5 x > 3 or x > 5 x > 3 or x < 5 x 5

14. Special Cases Intersections: x 5 Unions: x 5

15. Name the inequality: state the solution set CW1 CW2 CW3 -3-201 -6-5-4-3-2 0.70.80.91.01.1

16. Find the solution set for the following: A.|x| > 3 B.|x| < 3 What is the difference between A & B? What can you infer about the solutions to absolute value inequalities?

17. Absolute Values Inequalities* Steps for solving absolute value inequalities: 1.Isolate the absolute value 2.Remove the abs. val. and set up two cases (positive and negative). 3.< and < are intersections (and) 4.> and > are unions (or)

18. Name the absolute value inequality ex1. ex2. 0 123 3 4 5 67

19. Name the absolute value inequality ex1. ex2. 2 3 456 -4 -3 -20

20. Solving Absolute Value Inequalities: Examples Ex1: | x + 2 | > 4 Ex2: | 2x – 1 | < 5 Ex3: -2| x + 1| + 4 > 0

21. Classwork 1-6 Practice (ODD problems)