# How do you solve 4x+6y=12 for x?

Feb 9, 2017

See the entire solution process below:

#### Explanation:

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

$4 x + 6 y - \textcolor{red}{6 y} = 12 - \textcolor{red}{6 y}$

$4 x + 0 = 12 - 6 y$

$4 x = 12 - 6 y$

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

$\frac{4 x}{\textcolor{red}{4}} = \frac{12 - 6 y}{\textcolor{red}{4}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}} x}{\cancel{\textcolor{red}{4}}} = \frac{12 - 6 y}{4}$

$x = \frac{12 - 6 y}{4}$

Or

$x = \frac{12}{4} - \frac{6}{4} y$

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

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

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