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 Dependent Variable

 Number of inequalities to solve: 23456789
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# Solving Absolute Value Equations

## Solving an Equation of the Form | z | = a

Example

Solve: -2|5x - 8| - 14 = 6

 Solution -2|5x - 8| - 14 = 6 Step 1 Isolate the absolute value. Add 14 to both sides. Divide both sides by -2. -2|5x - 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, -2|5x - 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. -3|x| = -12 |x| = 4

The solutions are x = -4 and x = 4.