# How do you solve 3/4x+7/12=1/9x+5/6?

Apr 14, 2018

$x = \frac{9}{23}$

#### Explanation:

$\frac{3}{4} x + \frac{7}{12} = \frac{1}{9} x + \frac{5}{6}$

Multiplying through by their LCM which is $36$

$36 \left(\frac{3}{4} x\right) + 36 \left(\frac{7}{12}\right) = 36 \left(\frac{1}{9} x\right) + 36 \left(\frac{5}{6}\right)$

$9 \left(3 x\right) + 3 \left(7\right) = 4 \left(1 x\right) + 6 \left(5\right)$

$27 x + 21 = 4 x + 30$

$27 x - 4 x = 30 - 21$

$23 x = 9$

$x = \frac{9}{23}$