Solve for y 11-12y=3+6x

$11 - 12 y = 3 + 6 x$

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

Subtract $11$ from both sides of the equation.

$- 12 y = 3 + 6 x - 11$

Subtract $11$ from $3$ .

$- 12 y = 6 x - 8$

Divide each term in $- 12 y = 6 x - 8$ by $- 12$ and simplify.

Divide each term in $- 12 y = 6 x - 8$ by $- 12$ .

$\frac{- 12 y}{- 12} = \frac{6 x}{- 12} + \frac{- 8}{- 12}$

Simplify the left side.

Cancel the common factor of $- 12$ .

Cancel the common factor.

$\frac{- 12 y}{- 12} = \frac{6 x}{- 12} + \frac{- 8}{- 12}$

Divide $y$ by $1$ .

$y = \frac{6 x}{- 12} + \frac{- 8}{- 12}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $6$ and $- 12$ .

Factor $6$ out of $6 x$ .

$y = \frac{6 (x)}{- 12} + \frac{- 8}{- 12}$

Cancel the common factors.

Factor $6$ out of $- 12$ .

$y = \frac{6 x}{6 \cdot - 2} + \frac{- 8}{- 12}$

Cancel the common factor.

$y = \frac{6 x}{6 \cdot - 2} + \frac{- 8}{- 12}$

Rewrite the expression.

$y = \frac{x}{- 2} + \frac{- 8}{- 12}$

Move the negative in front of the fraction.

$y = - \frac{x}{2} + \frac{- 8}{- 12}$

Cancel the common factor of $- 8$ and $- 12$ .

Factor $- 4$ out of $- 8$ .

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

Cancel the common factors.

Factor $- 4$ out of $- 12$ .

$y = - \frac{x}{2} + \frac{- 4 \cdot 2}{- 4 \cdot 3}$

Cancel the common factor.

$y = - \frac{x}{2} + \frac{- 4 \cdot 2}{- 4 \cdot 3}$

Rewrite the expression.

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