# How do you solve for y in 3+6x = 11-4y?

Mar 20, 2017

See the entire solution process below:

#### Explanation:

First, subtract $\textcolor{red}{11}$ from each side of the equation to isolate the $y$ term while keeping the equation balanced:

$- \textcolor{red}{11} + 3 + 6 x = - \textcolor{red}{11} + 11 - 4 y$

$- 8 + 6 x = 0 - 4 y$

$- 8 + 6 x = - 4 y$

Now, divide each side of the equation by $\textcolor{red}{- 4}$ to solve for $y$ while keeping the equation balanced:

$\frac{- 8 + 6 x}{\textcolor{red}{- 4}} = \frac{- 4 y}{\textcolor{red}{- 4}}$

$\frac{- 8}{\textcolor{red}{- 4}} + \frac{6 x}{\textcolor{red}{- 4}} = \frac{\textcolor{red}{\cancel{\textcolor{B l a c k}{- 4}}} y}{\cancel{\textcolor{red}{- 4}}}$

$2 - \frac{6}{4} x = y$

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

$2 - \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} \times 3}{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} \times 2} x = y$

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

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

Or

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