## 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

- If the sign was already negative then there are

- Write the equation
- Solve both equations.

## Examples:

### Solve:

- |5x −3| + 7 = 42

- |6 −3x| − 2 = 12