Solve for x |4x-8|-2=2x

$| 4 x - 8 | - 2 = 2 x$

Step 1

Add $2$ to both sides of the equation.

$| 4 x - 8 | = 2 x + 2$

Step 2

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

$4 x - 8 = \pm (2 x + 2)$

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.

$4 x - 8 = 2 x + 2$

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

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

$4 x - 8 - 2 x = 2$

Subtract $2 x$ from $4 x$ .

$2 x - 8 = 2$

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

Add $8$ to both sides of the equation.

$2 x = 2 + 8$

Add $2$ and $8$ .

$2 x = 10$

Divide each term in $2 x = 10$ by $2$ and simplify.

Divide each term in $2 x = 10$ by $2$ .

$\frac{2 x}{2} = \frac{10}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{10}{2}$

Divide $x$ by $1$ .

$x = \frac{10}{2}$

Simplify the right side.

Divide $10$ by $2$ .

$x = 5$

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

$4 x - 8 = - (2 x + 2)$

Simplify $- (2 x + 2)$ .

Rewrite.

$4 x - 8 = 0 + 0 - (2 x + 2)$

Simplify by adding zeros.

$4 x - 8 = - (2 x + 2)$

Apply the distributive property.

$4 x - 8 = - (2 x) - 1 \cdot 2$

Multiply.

Multiply $2$ by $- 1$ .

$4 x - 8 = - 2 x - 1 \cdot 2$

Multiply $- 1$ by $2$ .

$4 x - 8 = - 2 x - 2$

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

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

$4 x - 8 + 2 x = - 2$

Add $4 x$ and $2 x$ .

$6 x - 8 = - 2$

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

Add $8$ to both sides of the equation.

$6 x = - 2 + 8$

Add $- 2$ and $8$ .

$6 x = 6$

Divide each term in $6 x = 6$ by $6$ and simplify.

Divide each term in $6 x = 6$ by $6$ .

$\frac{6 x}{6} = \frac{6}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x}{6} = \frac{6}{6}$

Divide $x$ by $1$ .

$x = \frac{6}{6}$

Simplify the right side.

Divide $6$ by $6$ .

$x = 1$

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

$x = 5, 1$

Solve for x |4x-8|-2=2x

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