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

$| - 2 x + 4 | = 4$

Step 1

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

$- 2 x + 4 = \pm 4$

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.

$- 2 x + 4 = 4$

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

Subtract $4$ from both sides of the equation.

$- 2 x = 4 - 4$

Subtract $4$ from $4$ .

$- 2 x = 0$

Divide each term in $- 2 x = 0$ by $- 2$ and simplify.

Divide each term in $- 2 x = 0$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{0}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{0}{- 2}$

Divide $x$ by $1$ .

$x = \frac{0}{- 2}$

Simplify the right side.

Divide $0$ by $- 2$ .

$x = 0$

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

$- 2 x + 4 = - 4$

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

Subtract $4$ from both sides of the equation.

$- 2 x = - 4 - 4$

Subtract $4$ from $- 4$ .

$- 2 x = - 8$

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.

$x = 0, 4$

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

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