Solve for x 6x+y=4x+11y

$6 x + y = 4 x + 11 y$

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

Subtract $4 x$ from both sides of the equation.

$6 x + y - 4 x = 11 y$

Subtract $4 x$ from $6 x$ .

$2 x + y = 11 y$

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

Subtract $y$ from both sides of the equation.

$2 x = 11 y - y$

Subtract $y$ from $11 y$ .

$2 x = 10 y$

Divide each term in $2 x = 10 y$ by $2$ and simplify.

Divide each term in $2 x = 10 y$ by $2$ .

$\frac{2 x}{2} = \frac{10 y}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{10 y}{2}$

Divide $x$ by $1$ .

$x = \frac{10 y}{2}$

Simplify the right side.

Cancel the common factor of $10$ and $2$ .

Factor $2$ out of $10 y$ .

$x = \frac{2 (5 y)}{2}$

Cancel the common factors.

Factor $2$ out of $2$ .

$x = \frac{2 (5 y)}{2 (1)}$

Cancel the common factor.

$x = \frac{2 (5 y)}{2 \cdot 1}$

Rewrite the expression.

$x = \frac{5 y}{1}$

Divide $5 y$ by $1$ .

$x = 5 y$