Solve for x |2(x-1)+4|=8

$| 2 (x - 1) + 4 | = 8$

Step 1

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

$2 (x - 1) + 4 = \pm 8$

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.

$2 (x - 1) + 4 = 8$

Simplify $2 (x - 1) + 4$ .

Simplify each term.

Apply the distributive property.

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

Multiply $2$ by $- 1$ .

$2 x - 2 + 4 = 8$

Add $- 2$ and $4$ .

$2 x + 2 = 8$

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

Subtract $2$ from both sides of the equation.

$2 x = 8 - 2$

Subtract $2$ from $8$ .

$2 x = 6$

Divide each term in $2 x = 6$ by $2$ and simplify.

Divide each term in $2 x = 6$ by $2$ .

$\frac{2 x}{2} = \frac{6}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{6}{2}$

Divide $x$ by $1$ .

$x = \frac{6}{2}$

Simplify the right side.

Divide $6$ by $2$ .

$x = 3$

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

$2 (x - 1) + 4 = - 8$

Simplify $2 (x - 1) + 4$ .

Simplify each term.

Apply the distributive property.

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

Multiply $2$ by $- 1$ .

$2 x - 2 + 4 = - 8$

Add $- 2$ and $4$ .

$2 x + 2 = - 8$

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

Subtract $2$ from both sides of the equation.

$2 x = - 8 - 2$

Subtract $2$ from $- 8$ .

$2 x = - 10$

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 $2$ .

$x = - 5$

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

$x = 3, - 5$

Solve for x |2(x-1)+4|=8

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