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

$| x + 2 | = 2 x + 4$

Step 1

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

$x + 2 = \pm (2 x + 4)$

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.

$x + 2 = 2 x + 4$

Move all terms containing $x$ to the left side of the equation.

Subtract $2 x$ from both sides of the equation.

$x + 2 - 2 x = 4$

Subtract $2 x$ from $x$ .

$- x + 2 = 4$

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

Subtract $2$ from both sides of the equation.

$- x = 4 - 2$

Subtract $2$ from $4$ .

$- x = 2$

Divide each term in $- x = 2$ by $- 1$ and simplify.

Divide each term in $- x = 2$ by $- 1$ .

$\frac{- x}{- 1} = \frac{2}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{2}{- 1}$

Divide $x$ by $1$ .

$x = \frac{2}{- 1}$

Simplify the right side.

Divide $2$ by $- 1$ .

$x = - 2$

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

$x + 2 = - (2 x + 4)$

Simplify $- (2 x + 4)$ .

Rewrite.

$x + 2 = 0 + 0 - (2 x + 4)$

Simplify by adding zeros.

$x + 2 = - (2 x + 4)$

Apply the distributive property.

$x + 2 = - (2 x) - 1 \cdot 4$

Multiply.

Multiply $2$ by $- 1$ .

$x + 2 = - 2 x - 1 \cdot 4$

Multiply $- 1$ by $4$ .

$x + 2 = - 2 x - 4$

Move all terms containing $x$ to the left side of the equation.

Add $2 x$ to both sides of the equation.

$x + 2 + 2 x = - 4$

Add $x$ and $2 x$ .

$3 x + 2 = - 4$

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

Subtract $2$ from both sides of the equation.

$3 x = - 4 - 2$

Subtract $2$ from $- 4$ .

$3 x = - 6$

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 $3$ .

$x = - 2$

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

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