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

##### 1 Answer

Aug 3, 2016

#### 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

#x/4 - 7/8 + (3x)/2 = 5/12 - (5x)/4#

can be rewritten as

#x/4 * 6/6 - 7/8 * 3/3 + (3x)/2 * 12/12 = 5/12 * 2/2 - (5x)/4 * 6/6#

This will get you

#(6x)/24 - 21/24 + (36x)/24 = 10/24 - (30x)/24#

Now you can focus on the *numerators*

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

Collect like terms to find

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

#72x = 31 implies x = 31/72#