Solve the Absolute Value Inequality for x |-6x|=30

$| - 6 x | = 30$

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

$- 6 x = \pm 30$

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.

$- 6 x = 30$

Divide each term in $- 6 x = 30$ by $- 6$ and simplify.

Divide each term in $- 6 x = 30$ by $- 6$ .

$\frac{- 6 x}{- 6} = \frac{30}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 x}{- 6} = \frac{30}{- 6}$

Divide $x$ by $1$ .

$x = \frac{30}{- 6}$

Simplify the right side.

Divide $30$ by $- 6$ .

$x = - 5$

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

$- 6 x = - 30$

Divide each term in $- 6 x = - 30$ by $- 6$ and simplify.

Divide each term in $- 6 x = - 30$ by $- 6$ .

$\frac{- 6 x}{- 6} = \frac{- 30}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 x}{- 6} = \frac{- 30}{- 6}$

Divide $x$ by $1$ .

$x = \frac{- 30}{- 6}$

Simplify the right side.

Divide $- 30$ by $- 6$ .

$x = 5$

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

$x = - 5, 5$