Solve for x x-4=1/4(8x-16)

$x - 4 = \frac{1}{4} (8 x - 16)$

Simplify $\frac{1}{4} \cdot (8 x - 16)$ .

Rewrite.

$x - 4 = 0 + 0 + \frac{1}{4} \cdot (8 x - 16)$

Simplify by adding zeros.

$x - 4 = \frac{1}{4} \cdot (8 x - 16)$

Apply the distributive property.

$x - 4 = \frac{1}{4} (8 x) + \frac{1}{4} \cdot - 16$

Cancel the common factor of $4$ .

Factor $4$ out of $8 x$ .

$x - 4 = \frac{1}{4} (4 (2 x)) + \frac{1}{4} \cdot - 16$

Cancel the common factor.

$x - 4 = \frac{1}{4} (4 (2 x)) + \frac{1}{4} \cdot - 16$

Rewrite the expression.

$x - 4 = 2 x + \frac{1}{4} \cdot - 16$

Cancel the common factor of $4$ .

Factor $4$ out of $- 16$ .

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

Cancel the common factor.

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

Rewrite the expression.

$x - 4 = 2 x - 4$

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

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

$x - 4 - 2 x = - 4$

Subtract $2 x$ from $x$ .

$- x - 4 = - 4$

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

Add $4$ to both sides of the equation.

$- x = - 4 + 4$

Add $- 4$ and $4$ .

$- x = 0$

Divide each term in $- x = 0$ by $- 1$ and simplify.

Divide each term in $- x = 0$ by $- 1$ .

$\frac{- x}{- 1} = \frac{0}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{0}{- 1}$

Divide $x$ by $1$ .

$x = \frac{0}{- 1}$

Simplify the right side.

Divide $0$ by $- 1$ .

$x = 0$