Solve the Absolute Value Inequality for c -9|c+8|=-99

$- 9 | c + 8 | = - 99$

Step 1

Divide each term in $- 9 | c + 8 | = - 99$ by $- 9$ and simplify.

Divide each term in $- 9 | c + 8 | = - 99$ by $- 9$ .

$\frac{- 9 | c + 8 |}{- 9} = \frac{- 99}{- 9}$

Simplify the left side.

Cancel the common factor of $- 9$ .

Cancel the common factor.

$\frac{- 9 | c + 8 |}{- 9} = \frac{- 99}{- 9}$

Divide $| c + 8 |$ by $1$ .

$| c + 8 | = \frac{- 99}{- 9}$

Simplify the right side.

Divide $- 99$ by $- 9$ .

$| c + 8 | = 11$

Step 2

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

$c + 8 = \pm 11$

Step 3

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.

$c + 8 = 11$

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

Subtract $8$ from both sides of the equation.

$c = 11 - 8$

Subtract $8$ from $11$ .

$c = 3$

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

$c + 8 = - 11$

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

Subtract $8$ from both sides of the equation.

$c = - 11 - 8$

Subtract $8$ from $- 11$ .

$c = - 19$

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

$c = 3, - 19$