Solve for x 15=5|3x+3|

$15 = 5 | 3 x + 3 |$

Step 1

Rewrite the equation as $5 | 3 x + 3 | = 15$ .

$5 | 3 x + 3 | = 15$

Step 2

Divide each term in $5 | 3 x + 3 | = 15$ by $5$ and simplify.

Divide each term in $5 | 3 x + 3 | = 15$ by $5$ .

$\frac{5 | 3 x + 3 |}{5} = \frac{15}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 | 3 x + 3 |}{5} = \frac{15}{5}$

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

$| 3 x + 3 | = \frac{15}{5}$

Simplify the right side.

Divide $15$ by $5$ .

$| 3 x + 3 | = 3$

Step 3

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

$3 x + 3 = \pm 3$

Step 4

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.

$3 x + 3 = 3$

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

Subtract $3$ from both sides of the equation.

$3 x = 3 - 3$

Subtract $3$ from $3$ .

$3 x = 0$

Divide each term in $3 x = 0$ by $3$ and simplify.

Divide each term in $3 x = 0$ by $3$ .

$\frac{3 x}{3} = \frac{0}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{0}{3}$

Divide $x$ by $1$ .

$x = \frac{0}{3}$

Simplify the right side.

Divide $0$ by $3$ .

$x = 0$

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

$3 x + 3 = - 3$

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

Subtract $3$ from both sides of the equation.

$3 x = - 3 - 3$

Subtract $3$ from $- 3$ .

$3 x = - 6$

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 $3$ .

$x = - 2$

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

$x = 0, - 2$

Solve for x 15=5|3x+3|

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