1. Objectives
Solve equations that contain absolute-value expressions.

2. What is absolute value?
Number’s distance from zero on a number line.
For example, |–5| = 5 and |5| = 5.
Because absolute value deals with distance – It cannot be negative!

3. Where is the absolute value button on my calculator???
TI 84 TI 83

4. Practice
= 4
= 8
= 5

5. Solving an Absolute-Value Equation
Get absolute value bars by itself on one side of the equals sign. (Everything must be inside the | | if not… MOVE IT!)
2. Rewrite as two cases.
Case 1: = Positive, Case 2: = Negative
3. Solve both cases.

6.
|x| – 3 = 4
│x + 2│= 16

7.
4│x│=8
2|x  1|=4

8.
│5x│=25
3|x + 7| = 24

9.
│2x│+1=9
│x+4│- 2 = 10

10. Not all absolute-value equations have two solutions.
If the absolute-value expression is positive there are two solutions.
EX: │x│=2 solutions are -2, 2
If the absolute-value expression equals 0, there is one solution.
EX: │x+1│=0 solution is -1
If an equation states that an absolute-value is negative, there are no solutions.
EX: │x│= no solutions

11.
8 + |x + 2| =  8
3 + |x + 4| = 0

12.
2  1|2x  5| = 7
6 + |x  4| = 6