1. 1-5 Absolute Value Equations
Objectives:
To solve absolute value equations

2. Absolute Value What is the definition of absolute value???
Distance from zero, so it’s always _________
How many numbers are the same distance from zero?
So every absolute value equation has two answers except…

3. Solving Equations with Absolute Values
Isolate the absolute value (get rid of outside numbers)
Split into two equations without the absolute value symbols
Solve the equations
2|3x +4| - 3 = 7

4. Examples
3|5x + 6|-7 = |6 - 2y| = 68

5. Question Is there a solution to 2|x| = -14?
So if an absolute value equals a negative number, there is no solution.

6. Definition
Extraneous Solution: a solution derived from a an original equation that is not a solution of the original equation.
It doesn’t work when you plug it in.

7. Variables on both sides
Solve and check for extraneous solutions. |2x + 3| = 3x + 2

8. Examples
|3x – 4| = –4x – 1 6|2x + 5| = 6x + 24

9. Example
⅔|3x – 6| = 4(x – 2)

10. Homework
Page 36, #1-15 odd, 35-43odd, 61,62