Solve for x 6+4|2x+6|=14

$6 + 4 | 2 x + 6 | = 14$

Move all terms not containing $| 2 x + 6 |$ to the right side of the equation.

Subtract $6$ from both sides of the equation.

$4 | 2 x + 6 | = 14 - 6$

Subtract $6$ from $14$ .

$4 | 2 x + 6 | = 8$

Divide each term in $4 | 2 x + 6 | = 8$ by $4$ and simplify.

Divide each term in $4 | 2 x + 6 | = 8$ by $4$ .

$\frac{4 | 2 x + 6 |}{4} = \frac{8}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 | 2 x + 6 |}{4} = \frac{8}{4}$

Divide $| 2 x + 6 |$ by $1$ .

$| 2 x + 6 | = \frac{8}{4}$

Simplify the right side.

Divide $8$ by $4$ .

$| 2 x + 6 | = 2$

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

$2 x + 6 = \pm 2$

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.

$2 x + 6 = 2$

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

Subtract $6$ from both sides of the equation.

$2 x = 2 - 6$

Subtract $6$ from $2$ .

$2 x = - 4$

Divide each term in $2 x = - 4$ by $2$ and simplify.

Divide each term in $2 x = - 4$ by $2$ .

$\frac{2 x}{2} = \frac{- 4}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 4}{2}$

Divide $x$ by $1$ .

$x = \frac{- 4}{2}$

Simplify the right side.

Divide $- 4$ by $2$ .

$x = - 2$

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

$2 x + 6 = - 2$

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

Subtract $6$ from both sides of the equation.

$2 x = - 2 - 6$

Subtract $6$ from $- 2$ .

$2 x = - 8$

Divide each term in $2 x = - 8$ by $2$ and simplify.

Divide each term in $2 x = - 8$ by $2$ .

$\frac{2 x}{2} = \frac{- 8}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 8}{2}$

Divide $x$ by $1$ .

$x = \frac{- 8}{2}$

Simplify the right side.

Divide $- 8$ by $2$ .

$x = - 4$

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

$x = - 2, - 4$

Solve for x 6+4|2x+6|=14

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