1. Absolute Value Inequalities

2. Absolute Value Inequalities
What does it mean when we solve an absolute value inequality?
We want to find the numbers that have, comparably, a distance greater than or smaller than the limit given.
Solve: |x| > 4
Start at 0.
Move 4 to the right. Which numbers have a distance greater than 4 away from zero?
Go back to 0.
Move 4 to the left. Which numbers have a distance greater than 4 away fro zero?
So, x could be the numbers to the right of 4 or the left of -4.

3. Solving Absolute Value Inequalities
To solve an absolute value Inequality:
Isolate the absolute value (get the absolute value by itself).
Create TWO inequalities using AND and OR by setting what is inside in relation to both the positive and negative value of the other side of the inequality.
“GREATOR” and “LESS THAND”
Greater Than requires an OR Statement…
Less Than requires an AND statement (compound inequality).
Solve the resulting inequality(-ies).
Check your answers by plugging in a sample number from the answer region(s) you found.

4. Example 1

5. Example 2

6. Example 3

7. Example 4

8. Example 5

9. Example 6