1. 5-5 Absolute Value Inequalities
Goal:
Solve absolute value inequalities.
Eligible Content:
A / A / A / A

2. Vocabulary Absolute Value – distance from zero
Every Absolute Value Inequality has TWO answers.

3. If | x |  8, then any number between 8 and 8 is a solution of the inequality.
 8  7  6  5  4  3  2 
AND problem

4. If | x | > 2, then any number bigger than 2 or less than -2 is a solution of the inequality.
 8  7  6  5  4  3  2 
OR problem

5. Every problem has 2 answers!
< and ≤ problems have AND solutions
> and ≥ problems have OR solutions

6. Solve |x+5|< 6
x + 5 can be any number between -6 and < x + 5 < < x < < x < 1

7. Solve | x  4 | > 3 OR x > 7 OR x < 1
x – 4 can be anything bigger than 3 or smaller than -3.
Positive x – 4 > x > 7 OR
Negative x – 4 < x < 1
x > 7 OR x < 1

8. Examples |x - 7|< 10 |x – 2|≥ 9 |5x + 8|≤ 12 |2x + 1| > 9
x ≥ 11 OR x ≤ -7
|5x + 8|≤ 12
-4 ≤ x ≤ 0.8
|2x + 1| > 9
x > 4 OR x < -5
|2x + 5|+ 1 ≤ 6
-5 ≤ x ≤ 0

9. Solve |p + 4| < 6. Then graph the solution set.
B. p > –10
C. –10 < p < 2
D. –2 < p < 10

10. Solve |2m – 2| > 6. Then graph the solution set.
A. m > –2 or m < 4
B. m > –2 or m > 4
C. –2 < m < 4
D. m < –2 or m > 4

11. Practice
Worksheet – “Tall Talent”

12. Special Problems Solve |p – 5| < –2 No solution Solve |5x – 1| ≥ –2
All real numbers

13. Homework Page 314 #8-18 even Solve and graph each solution!
Each problem should have 2 answers!!