Solve the Absolute Value Inequality for k |-8k|=24

$| - 8 k | = 24$

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

$- 8 k = \pm 24$

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.

$- 8 k = 24$

Divide each term in $- 8 k = 24$ by $- 8$ and simplify.

Divide each term in $- 8 k = 24$ by $- 8$ .

$\frac{- 8 k}{- 8} = \frac{24}{- 8}$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$\frac{- 8 k}{- 8} = \frac{24}{- 8}$

Divide $k$ by $1$ .

$k = \frac{24}{- 8}$

Simplify the right side.

Divide $24$ by $- 8$ .

$k = - 3$

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

$- 8 k = - 24$

Divide each term in $- 8 k = - 24$ by $- 8$ and simplify.

Divide each term in $- 8 k = - 24$ by $- 8$ .

$\frac{- 8 k}{- 8} = \frac{- 24}{- 8}$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$\frac{- 8 k}{- 8} = \frac{- 24}{- 8}$

Divide $k$ by $1$ .

$k = \frac{- 24}{- 8}$

Simplify the right side.

Divide $- 24$ by $- 8$ .

$k = 3$

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

$k = - 3, 3$