# How do you solve 3/2+3/4a=1/4a-1/2?

Feb 10, 2017

See the entire solution process below:

#### Explanation:

First, subtract $\textcolor{red}{\frac{3}{2}}$ and $\textcolor{b l u e}{\frac{1}{4} a}$ from each side of the equation to isolate the $a$ term while keeping the equation balanced:

$\frac{3}{2} + \frac{3}{4} a - \textcolor{red}{\frac{3}{2}} - \textcolor{b l u e}{\frac{1}{4} a} = \frac{1}{4} a - \frac{1}{2} - \textcolor{red}{\frac{3}{2}} - \textcolor{b l u e}{\frac{1}{4} a}$

$\frac{3}{2} - \textcolor{red}{\frac{3}{2}} + \frac{3}{4} a - \textcolor{b l u e}{\frac{1}{4} a} = \frac{1}{4} a - \textcolor{b l u e}{\frac{1}{4} a} - \frac{1}{2} - \textcolor{red}{\frac{3}{2}}$

$0 + \left(\frac{3}{4} - \textcolor{b l u e}{\frac{1}{4}}\right) a = 0 - \frac{1}{2} - \textcolor{red}{\frac{3}{2}}$

$\frac{2}{4} a = - \frac{4}{2}$

Now, multiply each side of the equation by $\frac{\textcolor{red}{4}}{\textcolor{b l u e}{2}}$ to solve for $a$ while keeping the equation balanced:

$\frac{\textcolor{red}{4}}{\textcolor{b l u e}{2}} \times \frac{2}{4} a = \frac{\textcolor{red}{4}}{\textcolor{b l u e}{2}} \times - \frac{4}{2}$

$\frac{8}{8} a = - \frac{16}{4}$

$1 a = - 4$

$a = - 4$