# How do you solve x/4 - 7/8 + 3/2x = 5/12 - 5/4x?

Aug 3, 2016

$x = \frac{31}{72}$

#### Explanation:

The first thing to do here is get rid of the denominators by finding the least common multiple, LCM, of all the numbers you have as denominators.

In this case, the LCM of

$2 , 4 , 8 , 12$

is $24$. This means that your starting equation

$\frac{x}{4} - \frac{7}{8} + \frac{3 x}{2} = \frac{5}{12} - \frac{5 x}{4}$

can be rewritten as

$\frac{x}{4} \cdot \frac{6}{6} - \frac{7}{8} \cdot \frac{3}{3} + \frac{3 x}{2} \cdot \frac{12}{12} = \frac{5}{12} \cdot \frac{2}{2} - \frac{5 x}{4} \cdot \frac{6}{6}$

This will get you

$\frac{6 x}{24} - \frac{21}{24} + \frac{36 x}{24} = \frac{10}{24} - \frac{30 x}{24}$

Now you can focus on the numerators

$6 x - 21 + 36 x = 10 - 30 x$

Collect like terms to find

$6 x + 36 x + 30 x = 10 + 21$

$72 x = 31 \implies x = \frac{31}{72}$