Solve for k |6-2k|=18

$| 6 - 2 k | = 18$

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

$6 - 2 k = \pm 18$

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.

$6 - 2 k = 18$

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

Subtract $6$ from both sides of the equation.

$- 2 k = 18 - 6$

Subtract $6$ from $18$ .

$- 2 k = 12$

Divide each term in $- 2 k = 12$ by $- 2$ and simplify.

Divide each term in $- 2 k = 12$ by $- 2$ .

$\frac{- 2 k}{- 2} = \frac{12}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 k}{- 2} = \frac{12}{- 2}$

Divide $k$ by $1$ .

$k = \frac{12}{- 2}$

Simplify the right side.

Divide $12$ by $- 2$ .

$k = - 6$

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

$6 - 2 k = - 18$

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

Subtract $6$ from both sides of the equation.

$- 2 k = - 18 - 6$

Subtract $6$ from $- 18$ .

$- 2 k = - 24$

Divide each term in $- 2 k = - 24$ by $- 2$ and simplify.

Divide each term in $- 2 k = - 24$ by $- 2$ .

$\frac{- 2 k}{- 2} = \frac{- 24}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 k}{- 2} = \frac{- 24}{- 2}$

Divide $k$ by $1$ .

$k = \frac{- 24}{- 2}$

Simplify the right side.

Divide $- 24$ by $- 2$ .

$k = 12$

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

$k = - 6, 12$