Solve for c -2|7-9c|+7=-15

$- 2 | 7 - 9 c | + 7 = - 15$

Step 1

Move all terms not containing $| 7 - 9 c |$ to the right side of the equation.

Subtract $7$ from both sides of the equation.

$- 2 | 7 - 9 c | = - 15 - 7$

Subtract $7$ from $- 15$ .

$- 2 | 7 - 9 c | = - 22$

Step 2

Divide each term in $- 2 | 7 - 9 c | = - 22$ by $- 2$ and simplify.

Divide each term in $- 2 | 7 - 9 c | = - 22$ by $- 2$ .

$\frac{- 2 | 7 - 9 c |}{- 2} = \frac{- 22}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 | 7 - 9 c |}{- 2} = \frac{- 22}{- 2}$

Divide $| 7 - 9 c |$ by $1$ .

$| 7 - 9 c | = \frac{- 22}{- 2}$

Simplify the right side.

Divide $- 22$ by $- 2$ .

$| 7 - 9 c | = 11$

Step 3

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

$7 - 9 c = \pm 11$

Step 4

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.

$7 - 9 c = 11$

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

Subtract $7$ from both sides of the equation.

$- 9 c = 11 - 7$

Subtract $7$ from $11$ .

$- 9 c = 4$

Divide each term in $- 9 c = 4$ by $- 9$ and simplify.

Divide each term in $- 9 c = 4$ by $- 9$ .

$\frac{- 9 c}{- 9} = \frac{4}{- 9}$

Simplify the left side.

Cancel the common factor of $- 9$ .

Cancel the common factor.

$\frac{- 9 c}{- 9} = \frac{4}{- 9}$

Divide $c$ by $1$ .

$c = \frac{4}{- 9}$

Simplify the right side.

Move the negative in front of the fraction.

$c = - \frac{4}{9}$

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

$7 - 9 c = - 11$

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

Subtract $7$ from both sides of the equation.

$- 9 c = - 11 - 7$

Subtract $7$ from $- 11$ .

$- 9 c = - 18$

Divide each term in $- 9 c = - 18$ by $- 9$ and simplify.

Divide each term in $- 9 c = - 18$ by $- 9$ .

$\frac{- 9 c}{- 9} = \frac{- 18}{- 9}$

Simplify the left side.

Cancel the common factor of $- 9$ .

Cancel the common factor.

$\frac{- 9 c}{- 9} = \frac{- 18}{- 9}$

Divide $c$ by $1$ .

$c = \frac{- 18}{- 9}$

Simplify the right side.

Divide $- 18$ by $- 9$ .

$c = 2$

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

$c = - \frac{4}{9}, 2$

Step 5

The result can be shown in multiple forms.

Exact Form:

$c = - \frac{4}{9}, 2$

Decimal Form:

$c = - 0.\overline{4}, 2$

Solve for c -2|7-9c|+7=-15

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