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

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

Step 1

Rewrite the equation as $2 | 6 x - 2 | = 8 x$ .

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

Step 2

Divide each term in $2 | 6 x - 2 | = 8 x$ by $2$ and simplify.

Divide each term in $2 | 6 x - 2 | = 8 x$ by $2$ .

$\frac{2 | 6 x - 2 |}{2} = \frac{8 x}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 | 6 x - 2 |}{2} = \frac{8 x}{2}$

Divide $| 6 x - 2 |$ by $1$ .

$| 6 x - 2 | = \frac{8 x}{2}$

Simplify the right side.

Cancel the common factor of $8$ and $2$ .

Factor $2$ out of $8 x$ .

$| 6 x - 2 | = \frac{2 (4 x)}{2}$

Cancel the common factors.

Factor $2$ out of $2$ .

$| 6 x - 2 | = \frac{2 (4 x)}{2 (1)}$

Cancel the common factor.

$| 6 x - 2 | = \frac{2 (4 x)}{2 \cdot 1}$

Rewrite the expression.

$| 6 x - 2 | = \frac{4 x}{1}$

Divide $4 x$ by $1$ .

$| 6 x - 2 | = 4 x$

Step 3

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

$6 x - 2 = \pm 4 x$

Step 4

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.

$6 x - 2 = 4 x$

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

Subtract $4 x$ from both sides of the equation.

$6 x - 2 - 4 x = 0$

Subtract $4 x$ from $6 x$ .

$2 x - 2 = 0$

Add $2$ to both sides of the equation.

$2 x = 2$

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

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

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $2$ by $2$ .

$x = 1$

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

$6 x - 2 = - 4 x$

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

Add $4 x$ to both sides of the equation.

$6 x - 2 + 4 x = 0$

Add $6 x$ and $4 x$ .

$10 x - 2 = 0$

Add $2$ to both sides of the equation.

$10 x = 2$

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

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

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

Simplify the left side.

Cancel the common factor of $10$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Cancel the common factor of $2$ and $10$ .

Factor $2$ out of $2$ .

$x = \frac{2 (1)}{10}$

Cancel the common factors.

Factor $2$ out of $10$ .

$x = \frac{2 \cdot 1}{2 \cdot 5}$

Cancel the common factor.

$x = \frac{2 \cdot 1}{2 \cdot 5}$

Rewrite the expression.

$x = \frac{1}{5}$

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

$x = 1, \frac{1}{5}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = 1, \frac{1}{5}$

Decimal Form:

$x = 1, 0.2$

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

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