Objective:

To solve absolute value equations.

Notes:

Absolute value equations can have zero, one, or two solutions.  There are two solutions for |x| = 7.  7 is a solution and so is −7.  Two solutions occur because both x and −(x) are solutions.

Steps to solve and absolute value equation:

  1. Isolate the absolute value part of the equation. (Get the absolute value part of the equation by itself on the left side.)
  2. Separate the equation into two parts:
    • Write the equation without the absolute value bars.
    • Write the word "or".
    • Write the equation without the absolute value bars again, but this time change the sign on the constant on the right side to negative.
      • If the sign was already negative then there are no solutions.
      • This is because the absolute value of an expression is always positive
  3. Solve both equations.

Examples:

Solve:

  1. |5x −3| + 7 = 42

    Ex 1

  2. |6 −3x| − 2 = 12

    Ex 1
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This page was last updated on 08/09/13.