Solve for c 42=|7c|

$42 = | 7 c |$

Rewrite the equation as $| 7 c | = 42$ .

$| 7 c | = 42$

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

$7 c = \pm 42$

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.

$7 c = 42$

Divide each term in $7 c = 42$ by $7$ and simplify.

Divide each term in $7 c = 42$ by $7$ .

$\frac{7 c}{7} = \frac{42}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 c}{7} = \frac{42}{7}$

Divide $c$ by $1$ .

$c = \frac{42}{7}$

Simplify the right side.

Divide $42$ by $7$ .

$c = 6$

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

$7 c = - 42$

Divide each term in $7 c = - 42$ by $7$ and simplify.

Divide each term in $7 c = - 42$ by $7$ .

$\frac{7 c}{7} = \frac{- 42}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 c}{7} = \frac{- 42}{7}$

Divide $c$ by $1$ .

$c = \frac{- 42}{7}$

Simplify the right side.

Divide $- 42$ by $7$ .

$c = - 6$

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

$c = 6, - 6$