Objectives Solve equations that contain absolute-value expressions.

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!

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

Practice = 4 = 8 = 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.

1. 2. |x| – 3 = 4 │x + 2│= 16

3. 4. 4│x│=8 2|x  1|=4

5. 6. │5x│=25 3|x + 7| = 24

7. 8. │2x│+1=9 │x+4│- 2 = 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│= -2 no solutions

9. 10. 8 + |x + 2| =  8 3 + |x + 4| = 0

11. 12. 2  1|2x  5| = 7 6 + |x  4| = 6