1. Solving Absolute Value Equations & Inequalities

2. Absolute Value (of x) Symbol lxl
The distance x is from 0 on the number line.
Always positive
Ex: l-3l=3

3. Ex: |x| = 5
What are the possible values of x?

4. Solve the following
|4-8|
|6-4|
|10+2|
2|6-8|
-4|-4+1|

5. To solve an absolute value equation:
|ax+b | = c, where c>0 To solve, set up 2 new equations, then solve each equation. ax+b = c or ax+b = -c ** make sure the absolute value is by itself before you split to solve.

6. Ex: Solve |6x-3| = 15

7. Ex: Solve |2x + 7| -3 = 8

8. Abs Value Inequalities
Absolute value inequalities can be represented by a conjunctions and disjunctions
Three different ways
|x|=a
X=-a or x=a

9. AND with LESS THAN |x|<a AND statement X>-a AND x<a
-a<x<a

10. OR with GREATER THAN
|x|>a
X<-a OR x>a

11. Solving abs value inequalities
Isolate the absolute value
Rewrite as a compound inequality
AND for less than, less than or equal to
OR for greater than, greater than or equal to
These abs value inequalities only have one variable (x) so they get graphed on a number line

12. Solve
|2x+1|>5

13. Solve
|4x|+16>8

14. Solve

15. Ex: Solve & graph.

16. Solve & graph.

17. Solving Absolute Value Inequalities
|ax+b| < c, where c>0
Becomes an “and” problem
Changes to: –c<ax+b<c
|ax+b| > c, where c>0
Becomes an “or” problem
Changes to: ax+b>c or ax+b<-c