# How do you solve  1/2-5/8x=7/8x+7/2?

Sep 29, 2017

See a solution process below:

#### Explanation:

First, multiply each side of the equation by $\textcolor{red}{8}$ to clear the fractions while keeping the equation balanced:

$\textcolor{red}{8} \left(\frac{1}{2} - \frac{5}{8} x\right) = \textcolor{red}{8} \left(\frac{7}{8} x + \frac{7}{2}\right)$

$\left(\textcolor{red}{8} \times \frac{1}{2}\right) - \left(\textcolor{red}{8} \times \frac{5}{8} x\right) = \left(\textcolor{red}{8} \times \frac{7}{8} x\right) + \left(\textcolor{red}{8} \times \frac{7}{2}\right)$

$\frac{\textcolor{red}{8}}{2} - \left(\cancel{\textcolor{red}{8}} \times \frac{5}{\textcolor{red}{\cancel{\textcolor{b l a c k}{8}}}} x\right) = \left(\cancel{\textcolor{red}{8}} \times \frac{7}{\textcolor{red}{\cancel{\textcolor{b l a c k}{8}}}} x\right) + \frac{56}{2}$

$4 - 5 x = 7 x + 28$

Next, add $\textcolor{red}{5 x}$ and subtract $\textcolor{b l u e}{28}$ from each side of the equation to isolate the $x$ term while keeping the equation balanced:

$4 - \textcolor{b l u e}{28} - 5 x + \textcolor{red}{5 x} = 7 x + \textcolor{red}{5 x} + 28 - \textcolor{b l u e}{28}$

$- 24 - 0 = \left(7 + \textcolor{red}{5}\right) x + 0$

$- 24 = 12 x$

Now, divide each side of the equation by $\textcolor{red}{12}$ to solve for $x$ while keeping the equation balanced:

$- \frac{24}{\textcolor{red}{12}} = \frac{12 x}{\textcolor{red}{12}}$

$- 2 = \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{12}}} x}{\cancel{\textcolor{red}{12}}}$

$- 2 = x$

$x = - 2$