Solving Absolute Value Equations
Solving an Equation of the Form  z  = a
Example
Solve: 25x  8  14 = 6
Solution 
25x  8  14 
= 6 
Step 1 Isolate the absolute value.
Add 14 to both sides.
Divide both sides by 2. 
25x  8
5x  8 
= 20
= 10 
Step 2 Make the substitution z =
5x  8. 
z 
= 10 
Since the absolute value of an expression cannot be equal to a
negative number, this equation has no solution.
Thus, 25x  8
 14 = 6 has no solution.
Note:
Be careful! An equation may have a
negative number on one side but still have
a solution. That is why it is important to
first isolate the absolute value.
For example, solve: Divide by 3.

3x = 12
x = 4 
The solutions are x = 4 and x = 4.
