Solve for x 2+5|3x+6|=62

$2 + 5 | 3 x + 6 | = 62$

Move all terms not containing $| 3 x + 6 |$ to the right side of the equation.

Subtract $2$ from both sides of the equation.

$5 | 3 x + 6 | = 62 - 2$

Subtract $2$ from $62$ .

$5 | 3 x + 6 | = 60$

Divide each term in $5 | 3 x + 6 | = 60$ by $5$ and simplify.

Divide each term in $5 | 3 x + 6 | = 60$ by $5$ .

$\frac{5 | 3 x + 6 |}{5} = \frac{60}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 | 3 x + 6 |}{5} = \frac{60}{5}$

Divide $| 3 x + 6 |$ by $1$ .

$| 3 x + 6 | = \frac{60}{5}$

Simplify the right side.

Divide $60$ by $5$ .

$| 3 x + 6 | = 12$

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

$3 x + 6 = \pm 12$

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.

$3 x + 6 = 12$

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

Subtract $6$ from both sides of the equation.

$3 x = 12 - 6$

Subtract $6$ from $12$ .

$3 x = 6$

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.

$3 x + 6 = - 12$

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

Subtract $6$ from both sides of the equation.

$3 x = - 12 - 6$

Subtract $6$ from $- 12$ .

$3 x = - 18$

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

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

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

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $- 18$ by $3$ .

$x = - 6$

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

$x = 2, - 6$

Solve for x 2+5|3x+6|=62

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