Solve for x |2x+6|-4=20

$| 2 x + 6 | - 4 = 20$

Step 1

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

Add $4$ to both sides of the equation.

$| 2 x + 6 | = 20 + 4$

Add $20$ and $4$ .

$| 2 x + 6 | = 24$

Step 2

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

$2 x + 6 = \pm 24$

Step 3

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.

$2 x + 6 = 24$

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

Subtract $6$ from both sides of the equation.

$2 x = 24 - 6$

Subtract $6$ from $24$ .

$2 x = 18$

Divide each term in $2 x = 18$ by $2$ and simplify.

Divide each term in $2 x = 18$ by $2$ .

$\frac{2 x}{2} = \frac{18}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{18}{2}$

Divide $x$ by $1$ .

$x = \frac{18}{2}$

Simplify the right side.

Divide $18$ by $2$ .

$x = 9$

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

$2 x + 6 = - 24$

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

Subtract $6$ from both sides of the equation.

$2 x = - 24 - 6$

Subtract $6$ from $- 24$ .

$2 x = - 30$

Divide each term in $2 x = - 30$ by $2$ and simplify.

Divide each term in $2 x = - 30$ by $2$ .

$\frac{2 x}{2} = \frac{- 30}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 30}{2}$

Divide $x$ by $1$ .

$x = \frac{- 30}{2}$

Simplify the right side.

Divide $- 30$ by $2$ .

$x = - 15$

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

$x = 9, - 15$

Solve for x |2x+6|-4=20

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