1. Absolute Value Equations and Inequalities
Lesson 3-6 (part 2)
Absolute Value Equations and Inequalities

2. What is absolute value? Remember:
Absolute value is the distance from Zero on a number line
 | x | = 3 

3. | x | < 3 (what values of x are less than 3 units away from 0?)
So what would this solution be?
 | x | < 3 (what values of x are less than 3 units away from 0?)
What would this solution be?
 | x | > 3 (what values of x are more than 3 units away from 0?)

4. *STEPS to solve an absolute value INEQUALITY:
Isolate the Absolute Value
Rewrite the absolute value equation as two separate equations, one positive and the other negative
FLIP THE SIGN FOR THE NEGATIVE CASE!
Solve each equation separately
After solving, substitute your answers back into original equation to verify that you solutions are valid

5. *STEPS to solve an absolute value INEQUALITY:
Solve and graph:
*STEPS to solve an absolute value INEQUALITY:
Isolate the Absolute Value
Rewrite the absolute value equation as two separate equations, one positive and the other negative
FLIP THE SIGN FOR THE NEGATIVE CASE!
Solve each equation separately
After solving, substitute your answers back into original equation to verify that you solutions are valid
My Turn: |x| ≥ 4
Your Turn: |x| < 0.5

6. *STEPS to solve an absolute value INEQUALITY:
Solve and graph:
*STEPS to solve an absolute value INEQUALITY:
Isolate the Absolute Value
Rewrite the absolute value equation as two separate equations, one positive and the other negative
FLIP THE SIGN FOR THE NEGATIVE CASE!
Solve each equation separately
After solving, substitute your answers back into original equation to verify that you solutions are valid
My Turn:
|2p + 5| >11
Your Turn:
|p – 4 | ≤ 21

7. *STEPS to solve an absolute value INEQUALITY:
Solve and graph:
*STEPS to solve an absolute value INEQUALITY:
Isolate the Absolute Value
Rewrite the absolute value equation as two separate equations, one positive and the other negative
FLIP THE SIGN FOR THE NEGATIVE CASE!
Solve each equation separately
After solving, substitute your answers back into original equation to verify that you solutions are valid
Your Turn:
|2x +1| > 13

8. Homework:
p. 170 #23-31
SimSo Lesson 24

9. Algebra Warm Up 03/11/15 1. | x | < 6 2. |2p + 5| >11
Solve:
 1. | x | < 6
2. |2p + 5| >11
 3. | x | + 1 < 3
|p – 4 | ≤ 21