Solve for x -2x-7y=y-4x

$- 2 x - 7 y = y - 4 x$

Step 1

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

Add $4 x$ to both sides of the equation.

$- 2 x - 7 y + 4 x = y$

Add $- 2 x$ and $4 x$ .

$2 x - 7 y = y$

Step 2

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

Add $7 y$ to both sides of the equation.

$2 x = y + 7 y$

Add $y$ and $7 y$ .

$2 x = 8 y$

Step 3

Divide each term in $2 x = 8 y$ by $2$ and simplify.

Divide each term in $2 x = 8 y$ by $2$ .

$\frac{2 x}{2} = \frac{8 y}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{8 y}{2}$

Divide $x$ by $1$ .

$x = \frac{8 y}{2}$

Simplify the right side.

Cancel the common factor of $8$ and $2$ .

Factor $2$ out of $8 y$ .

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

Cancel the common factors.

Factor $2$ out of $2$ .

$x = \frac{2 (4 y)}{2 (1)}$

Cancel the common factor.

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

Rewrite the expression.

$x = \frac{4 y}{1}$

Divide $4 y$ by $1$ .

$x = 4 y$