Solve for x 6+|2x-6|=8

$6 + | 2 x - 6 | = 8$

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

Subtract $6$ from both sides of the equation.

$| 2 x - 6 | = 8 - 6$

Subtract $6$ from $8$ .

$| 2 x - 6 | = 2$

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.

Add $6$ to both sides of the equation.

$2 x = 2 + 6$

Add $2$ and $6$ .

$2 x = 8$

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 $2$ .

$x = 4$

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.

Add $6$ to both sides of the equation.

$2 x = - 2 + 6$

Add $- 2$ and $6$ .

$2 x = 4$

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 $2$ .

$x = 2$

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

$x = 4, 2$

Solve for x 6+|2x-6|=8

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