How do you solve 12x=2y-6 for y?

Apr 7, 2017

See the entire solution process below:

Explanation:

First, add $\textcolor{red}{6}$ to each side of the equation to isolate the $y$ term while keeping the equation balanced:

$12 x + \textcolor{red}{6} = 2 y - 6 + \textcolor{red}{6}$

$12 x + 6 = 2 y - 0$

$12 x + 6 = 2 y$

Next, multiply each side of the equation by $\textcolor{red}{\frac{1}{2}}$ to solve for $y$ while keeping the equation balanced:

$\textcolor{red}{\frac{1}{2}} \left(12 x + 6\right) = \textcolor{red}{\frac{1}{2}} \times 2 y$

$\left(\textcolor{red}{\frac{1}{2}} \times 12 x\right) + \left(\textcolor{red}{\frac{1}{2}} \times 6\right) = \textcolor{red}{\frac{1}{\textcolor{b l a c k}{\cancel{\textcolor{red}{2}}}}} \times \textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} y$

$6 x + 3 = y$

$y = 6 x + 3$