Solve for x |6-4x|=8

$| 6 - 4 x | = 8$

Step 1

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

$6 - 4 x = \pm 8$

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.

$6 - 4 x = 8$

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

Subtract $6$ from both sides of the equation.

$- 4 x = 8 - 6$

Subtract $6$ from $8$ .

$- 4 x = 2$

Divide each term in $- 4 x = 2$ by $- 4$ and simplify.

Divide each term in $- 4 x = 2$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{2}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{2}{- 4}$

Divide $x$ by $1$ .

$x = \frac{2}{- 4}$

Simplify the right side.

Cancel the common factor of $2$ and $- 4$ .

Factor $2$ out of $2$ .

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

Cancel the common factors.

Factor $2$ out of $- 4$ .

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

Cancel the common factor.

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

Rewrite the expression.

$x = \frac{1}{- 2}$

Move the negative in front of the fraction.

$x = - \frac{1}{2}$

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

$6 - 4 x = - 8$

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

Subtract $6$ from both sides of the equation.

$- 4 x = - 8 - 6$

Subtract $6$ from $- 8$ .

$- 4 x = - 14$

Divide each term in $- 4 x = - 14$ by $- 4$ and simplify.

Divide each term in $- 4 x = - 14$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{- 14}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{- 14}{- 4}$

Divide $x$ by $1$ .

$x = \frac{- 14}{- 4}$

Simplify the right side.

Cancel the common factor of $- 14$ and $- 4$ .

Factor $- 2$ out of $- 14$ .

$x = \frac{- 2 (7)}{- 4}$

Cancel the common factors.

Factor $- 2$ out of $- 4$ .

$x = \frac{- 2 \cdot 7}{- 2 \cdot 2}$

Cancel the common factor.

$x = \frac{- 2 \cdot 7}{- 2 \cdot 2}$

Rewrite the expression.

$x = \frac{7}{2}$

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

$x = - \frac{1}{2}, \frac{7}{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{1}{2}, \frac{7}{2}$

Decimal Form:

$x = - 0.5, 3.5$

Mixed Number Form:

$x = - \frac{1}{2}, 3 \frac{1}{2}$

Solve for x |6-4x|=8

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