1. Unit 3- Lesson 5.6 Absolute Value Inequalities
Objective: SWBAT solve and graph absolute value inequalities on a number line.

2. Review: |x|=3 means the distance between x and 0 is 3.
The inequality |x|<3 means the distance between x and 0 is less than 3.
The inequality |x|>3 means the distance between x and 0 is greater than 3.

3. Solve Absolute Value Inequalities
|x|≥6
The distance between x and 0 is greater than or equal to 6, so x≤-6 OR x≥6
b. |x|≤ 0.5
The distance between x and 0.5 is less than or equal to 0.5 So -0.5≤x≤0.5

4. What can we conclude from those two examples?
**If you are given |x|> a number or |x|≥ a number you should write this as an OR compound inequality Ex) |x|>2 you write as x<-2 OR x >2 **if you are given |x|< a number or |x|≤a number you should write this as an AND compound inequality Ex) |x|<2 you write as -2<x<2

5. Try these on your own & graph
|x|≤ 8
|x|<3
|x|> 4

6. Solve it! |x-5|≥7 Step 1: rewrite as a compound inequality
* Since it is a ≥ inequality write it as an OR compound inequality
Step 1: rewrite as a compound inequality
X-5≤-7 OR x-5≥7
Step 2: solve for x
X≤ -2 OR X≥12
Step 3: Graph it on a number line:

7. Solve and graph the following: |-1x-5|+3 <9 Step 1: Subtract 3 from both sides |-1x-5|< 6 Step 2: Since < write this as AND compound inequality -6< -1x-5 < 6 Step 3: Add five to all sides -1<-1x<11 Step 4: Divide all sides by -1 (don’t forget to flip the signs!!) 1>x>-11 Step 5: Graph it on a number line!

8. Practice!
|x+3| >8

9. And Another
|2x-1|<11

10. Last one!
3|5x-6|-8≤ 13