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

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.

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

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

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

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:

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!

Practice! |x+3| >8

And Another |2x-1|<11

Last one! 3|5x-6|-8≤ 13