Solve for x x-4=1/3(6x-54)

$x - 4 = \frac{1}{3} (6 x - 54)$

Simplify $\frac{1}{3} \cdot (6 x - 54)$ .

Rewrite.

$x - 4 = 0 + 0 + \frac{1}{3} \cdot (6 x - 54)$

Simplify by adding zeros.

$x - 4 = \frac{1}{3} \cdot (6 x - 54)$

Apply the distributive property.

$x - 4 = \frac{1}{3} (6 x) + \frac{1}{3} \cdot - 54$

Cancel the common factor of $3$ .

Factor $3$ out of $6 x$ .

$x - 4 = \frac{1}{3} (3 (2 x)) + \frac{1}{3} \cdot - 54$

Cancel the common factor.

$x - 4 = \frac{1}{3} (3 (2 x)) + \frac{1}{3} \cdot - 54$

Rewrite the expression.

$x - 4 = 2 x + \frac{1}{3} \cdot - 54$

Cancel the common factor of $3$ .

Factor $3$ out of $- 54$ .

$x - 4 = 2 x + \frac{1}{3} \cdot (3 (- 18))$

Cancel the common factor.

$x - 4 = 2 x + \frac{1}{3} \cdot (3 \cdot - 18)$

Rewrite the expression.

$x - 4 = 2 x - 18$

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

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

$x - 4 - 2 x = - 18$

Subtract $2 x$ from $x$ .

$- x - 4 = - 18$

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

Add $4$ to both sides of the equation.

$- x = - 18 + 4$

Add $- 18$ and $4$ .

$- x = - 14$

Divide each term in $- x = - 14$ by $- 1$ and simplify.

Divide each term in $- x = - 14$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 14}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 14}{- 1}$

Divide $x$ by $1$ .

$x = \frac{- 14}{- 1}$

Simplify the right side.

Divide $- 14$ by $- 1$ .

$x = 14$