# How do you solve 5/4x + 1/8x = 9/8 + x?

Apr 13, 2018

$x = 3$

#### Explanation:

First, multiply the whole equation by $8$

$8 \left[\frac{5}{4} x + \frac{1}{8} x = \frac{9}{8} + x\right]$

$8 \frac{5}{4} x + 8 \frac{1}{8} x = 8 \frac{9}{8} + \left(8\right) x$

$\cancel{8} \textcolor{red}{2} \frac{5}{\cancel{4}} x + \cancel{8} \frac{1}{\cancel{8}} x = \cancel{8} \frac{9}{\cancel{8}} + \left(8\right) x$

$10 x + x = 9 + 8 x$

$11 x = 9 + 8 x$

Now subtract $8 x$ from each side

$11 x - 8 x = 9 + 8 x - 8 x$

$3 x = 9$

Now divide each side by $3$

$\frac{3}{3} x = \frac{9}{3}$

$x = 3$

$x = 3$