Solve for x 12-2x=-2(y-x)

$12 - 2 x = - 2 (y - x)$

Step 1

Simplify $- 2 (y - x)$ .

Rewrite.

$12 - 2 x = 0 + 0 - 2 (y - x)$

Simplify by adding zeros.

$12 - 2 x = - 2 (y - x)$

Apply the distributive property.

$12 - 2 x = - 2 y - 2 (- x)$

Multiply $- 1$ by $- 2$ .

$12 - 2 x = - 2 y + 2 x$

Step 2

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

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

$12 - 2 x - 2 x = - 2 y$

Subtract $2 x$ from $- 2 x$ .

$12 - 4 x = - 2 y$

Step 3

Subtract $12$ from both sides of the equation.

$- 4 x = - 2 y - 12$

Step 4

Divide each term in $- 4 x = - 2 y - 12$ by $- 4$ and simplify.

Divide each term in $- 4 x = - 2 y - 12$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{- 2 y}{- 4} + \frac{- 12}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{- 2 y}{- 4} + \frac{- 12}{- 4}$

Divide $x$ by $1$ .

$x = \frac{- 2 y}{- 4} + \frac{- 12}{- 4}$

Simplify the right side.

Simplify each term.

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

Factor $- 2$ out of $- 2 y$ .

$x = \frac{- 2 (y)}{- 4} + \frac{- 12}{- 4}$

Cancel the common factors.

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

$x = \frac{- 2 (y)}{- 2 (2)} + \frac{- 12}{- 4}$

Cancel the common factor.

$x = \frac{- 2 y}{- 2 \cdot 2} + \frac{- 12}{- 4}$

Rewrite the expression.

$x = \frac{y}{2} + \frac{- 12}{- 4}$

Divide $- 12$ by $- 4$ .

$x = \frac{y}{2} + 3$