Solve for x 1/3(12x-12)=10+2x

$\frac{1}{3} (12 x - 12) = 10 + 2 x$

Simplify $\frac{1}{3} \cdot (12 x - 12)$ .

Rewrite.

$0 + 0 + \frac{1}{3} \cdot (12 x - 12) = 10 + 2 x$

Simplify by adding zeros.

$\frac{1}{3} \cdot (12 x - 12) = 10 + 2 x$

Apply the distributive property.

$\frac{1}{3} (12 x) + \frac{1}{3} \cdot - 12 = 10 + 2 x$

Cancel the common factor of $3$ .

Factor $3$ out of $12 x$ .

$\frac{1}{3} (3 (4 x)) + \frac{1}{3} \cdot - 12 = 10 + 2 x$

Cancel the common factor.

$\frac{1}{3} (3 (4 x)) + \frac{1}{3} \cdot - 12 = 10 + 2 x$

Rewrite the expression.

$4 x + \frac{1}{3} \cdot - 12 = 10 + 2 x$

Cancel the common factor of $3$ .

Factor $3$ out of $- 12$ .

$4 x + \frac{1}{3} \cdot (3 (- 4)) = 10 + 2 x$

Cancel the common factor.

$4 x + \frac{1}{3} \cdot (3 \cdot - 4) = 10 + 2 x$

Rewrite the expression.

$4 x - 4 = 10 + 2 x$

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

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

$4 x - 4 - 2 x = 10$

Subtract $2 x$ from $4 x$ .

$2 x - 4 = 10$

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

Add $4$ to both sides of the equation.

$2 x = 10 + 4$

Add $10$ and $4$ .

$2 x = 14$

Divide each term in $2 x = 14$ by $2$ and simplify.

Divide each term in $2 x = 14$ by $2$ .

$\frac{2 x}{2} = \frac{14}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{14}{2}$

Divide $x$ by $1$ .

$x = \frac{14}{2}$

Simplify the right side.

Divide $14$ by $2$ .

$x = 7$