Solve the Absolute Value Inequality for x 3|x-3|=18

$3 | x - 3 | = 18$

Divide each term in $3 | x - 3 | = 18$ by $3$ and simplify.

Divide each term in $3 | x - 3 | = 18$ by $3$ .

$\frac{3 | x - 3 |}{3} = \frac{18}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 | x - 3 |}{3} = \frac{18}{3}$

Divide $| x - 3 |$ by $1$ .

$| x - 3 | = \frac{18}{3}$

Simplify the right side.

Divide $18$ by $3$ .

$| x - 3 | = 6$

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

$x - 3 = \pm 6$

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.

$x - 3 = 6$

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

Add $3$ to both sides of the equation.

$x = 6 + 3$

Add $6$ and $3$ .

$x = 9$

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

$x - 3 = - 6$

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

Add $3$ to both sides of the equation.

$x = - 6 + 3$

Add $- 6$ and $3$ .

$x = - 3$

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

$x = 9, - 3$