4.8  Solving Absolute Value Equations

Mrs. Agriesti's Algebra

Goal: To learn to solve absolute value equations.

To solve and absolute value equation:

1.    Get the absolute value part of the equation by itself on the left side.
2.    A. Write the equation without the absolute value bars.
       B. Write the word "or".
       C. Write the equation without the absolute value bars again, but this time change the sign on the constant on the right side (if it is positive change it to negative; if negative, change to positive).
3.    Solve both equations.

Ex:    |5x - 3| + 7 = 42
                       -7     -7
                |5x - 3| = 35
                 5x - 3  = 35   or    5x - 3 = -35
                     + 3    + 3              + 3    + 3 
                 5x       = 38           5x      = -32 
                 5x       = 38           5x      = -32

                  5            5             5             5
                          x = 38/5              x = - 32/5


Ex:    |6 - 3x| - 2 = 12 
                    + 2   + 2
         |6 - 3x|       = 14
                 6 - 3x = 14   or    6 - 3x = -14   
                -6          - 6         - 6            - 6   
                    - 3x =   8             - 3x = -20 
                    - 3x =   8              -3x = -20 
                     - 3      -3             - 3      - 3
                        x = -8/3              x = 20/3

Get the absolute value part by itself.

Write without the absolute value bars (twice) with the word "or" between them.  Don't forget to change the sign on the right side of the second equation to negative.

Get the absolute value part by itself.

Write without the absolute value bars (twice) with the word "or" between them.  Don't forget to change the sign on the right side of the second equation to negative.

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