Solve the Absolute Value Inequality for q |q-8|=14

$| q - 8 | = 14$

Step 1

Remove the absolute value term. This creates a $\pm$ on the right side of the equation because $| x | = \pm x$ .

$q - 8 = \pm 14$

Step 2

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$q - 8 = 14$

Move all terms not containing $q$ to the right side of the equation.

Add $8$ to both sides of the equation.

$q = 14 + 8$

Add $14$ and $8$ .

$q = 22$

Next, use the negative value of the $\pm$ to find the second solution.

$q - 8 = - 14$

Move all terms not containing $q$ to the right side of the equation.

Add $8$ to both sides of the equation.

$q = - 14 + 8$

Add $- 14$ and $8$ .

$q = - 6$

The complete solution is the result of both the positive and negative portions of the solution.

$q = 22, - 6$