Solve for x |3x-3|=18

$| 3 x - 3 | = 18$

Step 1

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

$3 x - 3 = \pm 18$

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.

$3 x - 3 = 18$

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

Add $3$ to both sides of the equation.

$3 x = 18 + 3$

Add $18$ and $3$ .

$3 x = 21$

Divide each term in $3 x = 21$ by $3$ and simplify.

Divide each term in $3 x = 21$ by $3$ .

$\frac{3 x}{3} = \frac{21}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{21}{3}$

Divide $x$ by $1$ .

$x = \frac{21}{3}$

Simplify the right side.

Divide $21$ by $3$ .

$x = 7$

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

$3 x - 3 = - 18$

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

Add $3$ to both sides of the equation.

$3 x = - 18 + 3$

Add $- 18$ and $3$ .

$3 x = - 15$

Divide each term in $3 x = - 15$ by $3$ and simplify.

Divide each term in $3 x = - 15$ by $3$ .

$\frac{3 x}{3} = \frac{- 15}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{- 15}{3}$

Divide $x$ by $1$ .

$x = \frac{- 15}{3}$

Simplify the right side.

Divide $- 15$ by $3$ .

$x = - 5$

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

$x = 7, - 5$

Solve for x |3x-3|=18

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