Solve for x |3x+12|=18

$| 3 x + 12 | = 18$

Step 1

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

$3 x + 12 = \pm 18$

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.

$3 x + 12 = 18$

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

Subtract $12$ from both sides of the equation.

$3 x = 18 - 12$

Subtract $12$ from $18$ .

$3 x = 6$

Divide each term in $3 x = 6$ by $3$ and simplify.

Divide each term in $3 x = 6$ by $3$ .

$\frac{3 x}{3} = \frac{6}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{6}{3}$

Divide $x$ by $1$ .

$x = \frac{6}{3}$

Simplify the right side.

Divide $6$ by $3$ .

$x = 2$

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

$3 x + 12 = - 18$

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

Subtract $12$ from both sides of the equation.

$3 x = - 18 - 12$

Subtract $12$ from $- 18$ .

$3 x = - 30$

Divide each term in $3 x = - 30$ by $3$ and simplify.

Divide each term in $3 x = - 30$ by $3$ .

$\frac{3 x}{3} = \frac{- 30}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{- 30}{3}$

Divide $x$ by $1$ .

$x = \frac{- 30}{3}$

Simplify the right side.

Divide $- 30$ by $3$ .

$x = - 10$

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

$x = 2, - 10$

Solve for x |3x+12|=18

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