Solve the Absolute Value Inequality for x |3x|=9

$| 3 x | = 9$

Step 1

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

$3 x = \pm 9$

Step 2

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.

$3 x = 9$

Divide each term in $3 x = 9$ by $3$ and simplify.

Divide each term in $3 x = 9$ by $3$ .

$\frac{3 x}{3} = \frac{9}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{9}{3}$

Divide $x$ by $1$ .

$x = \frac{9}{3}$

Simplify the right side.

Divide $9$ by $3$ .

$x = 3$

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

$3 x = - 9$

Divide each term in $3 x = - 9$ by $3$ and simplify.

Divide each term in $3 x = - 9$ by $3$ .

$\frac{3 x}{3} = \frac{- 9}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{- 9}{3}$

Divide $x$ by $1$ .

$x = \frac{- 9}{3}$

Simplify the right side.

Divide $- 9$ by $3$ .

$x = - 3$

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

$x = 3, - 3$