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:
- Isolate the absolute value part of the equation. (Get the absolute value part of the equation by itself on the left side.)
- 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
- Solve both equations.
Examples:
Solve:
- |5x −3| + 7 = 42
- |6 −3x| − 2 = 12
