Solve for k 8-12|k+5|=-4

$8 - 12 | k + 5 | = - 4$

Move all terms not containing $| k + 5 |$ to the right side of the equation.

Subtract $8$ from both sides of the equation.

$- 12 | k + 5 | = - 4 - 8$

Subtract $8$ from $- 4$ .

$- 12 | k + 5 | = - 12$

Divide each term in $- 12 | k + 5 | = - 12$ by $- 12$ and simplify.

Divide each term in $- 12 | k + 5 | = - 12$ by $- 12$ .

$\frac{- 12 | k + 5 |}{- 12} = \frac{- 12}{- 12}$

Simplify the left side.

Cancel the common factor of $- 12$ .

Cancel the common factor.

$\frac{- 12 | k + 5 |}{- 12} = \frac{- 12}{- 12}$

Divide $| k + 5 |$ by $1$ .

$| k + 5 | = \frac{- 12}{- 12}$

Simplify the right side.

Divide $- 12$ by $- 12$ .

$| k + 5 | = 1$

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

$k + 5 = \pm 1$

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.

$k + 5 = 1$

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

Subtract $5$ from both sides of the equation.

$k = 1 - 5$

Subtract $5$ from $1$ .

$k = - 4$

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

$k + 5 = - 1$

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

Subtract $5$ from both sides of the equation.

$k = - 1 - 5$

Subtract $5$ from $- 1$ .

$k = - 6$

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

$k = - 4, - 6$