Solve for c 9=|-c+12|

$9 = | - c + 12 |$

Step 1

Rewrite the equation as $| - c + 12 | = 9$ .

$| - c + 12 | = 9$

Step 2

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

$- c + 12 = \pm 9$

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.

$- c + 12 = 9$

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

Subtract $12$ from both sides of the equation.

$- c = 9 - 12$

Subtract $12$ from $9$ .

$- c = - 3$

Divide each term in $- c = - 3$ by $- 1$ and simplify.

Divide each term in $- c = - 3$ by $- 1$ .

$\frac{- c}{- 1} = \frac{- 3}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{c}{1} = \frac{- 3}{- 1}$

Divide $c$ by $1$ .

$c = \frac{- 3}{- 1}$

Simplify the right side.

Divide $- 3$ by $- 1$ .

$c = 3$

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

$- c + 12 = - 9$

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

Subtract $12$ from both sides of the equation.

$- c = - 9 - 12$

Subtract $12$ from $- 9$ .

$- c = - 21$

Divide each term in $- c = - 21$ by $- 1$ and simplify.

Divide each term in $- c = - 21$ by $- 1$ .

$\frac{- c}{- 1} = \frac{- 21}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{c}{1} = \frac{- 21}{- 1}$

Divide $c$ by $1$ .

$c = \frac{- 21}{- 1}$

Simplify the right side.

Divide $- 21$ by $- 1$ .

$c = 21$

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

$c = 3, 21$

Solve for c 9=|-c+12|

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