Solve for x -1/3x+12=-2x+2

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

Combine $x$ and $\frac{1}{3}$ .

$- \frac{x}{3} + 12 = - 2 x + 2$

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

Add $2 x$ to both sides of the equation.

$- \frac{x}{3} + 12 + 2 x = 2$

To write $2 x$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Combine $2 x$ and $\frac{3}{3}$ .

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

Combine the numerators over the common denominator.

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

Simplify each term.

Simplify the numerator.

Factor $x$ out of $- x + 2 x \cdot 3$ .

Factor $x$ out of $- x$ .

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

Factor $x$ out of $2 x \cdot 3$ .

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

Factor $x$ out of $x \cdot - 1 + x (2 \cdot 3)$ .

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

Multiply $2$ by $3$ .

$\frac{x (- 1 + 6)}{3} + 12 = 2$

Add $- 1$ and $6$ .

$\frac{x \cdot 5}{3} + 12 = 2$

Move $5$ to the left of $x$ .

$\frac{5 x}{3} + 12 = 2$

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

Subtract $12$ from both sides of the equation.

$\frac{5 x}{3} = 2 - 12$

Subtract $12$ from $2$ .

$\frac{5 x}{3} = - 10$

Multiply both sides of the equation by $\frac{3}{5}$ .

$\frac{3}{5} \cdot \frac{5 x}{3} = \frac{3}{5} \cdot - 10$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{3}{5} \cdot \frac{5 x}{3}$ .

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3}{5} \cdot \frac{5 x}{3} = \frac{3}{5} \cdot - 10$

Rewrite the expression.

$\frac{1}{5} (5 x) = \frac{3}{5} \cdot - 10$

Cancel the common factor of $5$ .

Factor $5$ out of $5 x$ .

$\frac{1}{5} (5 (x)) = \frac{3}{5} \cdot - 10$

Cancel the common factor.

$\frac{1}{5} (5 x) = \frac{3}{5} \cdot - 10$

Rewrite the expression.

$x = \frac{3}{5} \cdot - 10$

Simplify the right side.

Simplify $\frac{3}{5} \cdot - 10$ .

Cancel the common factor of $5$ .

Factor $5$ out of $- 10$ .

$x = \frac{3}{5} \cdot (5 (- 2))$

Cancel the common factor.

$x = \frac{3}{5} \cdot (5 \cdot - 2)$

Rewrite the expression.

$x = 3 \cdot - 2$

Multiply $3$ by $- 2$ .

$x = - 6$

Solve for x -1/3x+12=-2x+2

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