# How do you solve 1/8x-3/4=7/16x+1/2?

Apr 9, 2017

See the entire solution process below:

#### Explanation:

First, multiply each side of the equation by $\textcolor{red}{16}$ to eliminate the fractions while keeping the equation balanced. $\textcolor{red}{16}$ is the Lowest Common Denominator of all the fractions:

$\textcolor{red}{16} \left(\frac{1}{8} x - \frac{3}{4}\right) = \textcolor{red}{16} \left(\frac{7}{16} x + \frac{1}{2}\right)$

(cancel(color(red)(16)) 2 xx 1/color(red)(cancel(color(black)(8)))x) - (cancel(color(red)(16)) 4 xx 3/color(red)(cancel(color(black)(4)))) = (cancel(color(red)(16)) xx 7/color(red)(cancel(color(black)(16)))x) + (cancel(color(red)(16)) 8 xx 1/color(red)(cancel(color(black)(2))))

$2 x - 12 = 7 x + 8$

Next, subtract $\textcolor{red}{2 x}$ and $\textcolor{b l u e}{8}$ from each side of the equation to isolate the $x$ term while keeping the equation balanced:

$- \textcolor{red}{2 x} + 2 x - 12 - \textcolor{b l u e}{8} = - \textcolor{red}{2 x} + 7 x + 8 - \textcolor{b l u e}{8}$

$0 - 20 = \left(- \textcolor{red}{2} + 7\right) x + 0$

$- 20 = 5 x$

Now, divide each side of the equation by $\textcolor{red}{5}$ to solve for $x$ while keeping the equation balanced:

$- \frac{20}{\textcolor{red}{5}} = \frac{5 x}{\textcolor{red}{5}}$

$- 4 = \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{5}}} x}{\cancel{\textcolor{red}{5}}}$

$- 4 = x$

$x = - 4$