Please solve for x, and give me an explanation on how you did so? 1/2x-1/3=5/6

Explanation:

Fractions are a pain to deal with, so whenever possible I recommend you eliminate them. With equations like this, you can multiply both sides by the same number to do so. The question is: which number would that be?

If you pick on the LCD, then you'll be able to clear out the fractions. The LCD of 1/2, 1/3, and 5/6 is 6 since the LCM of the denominators is 6.

Multiply both sides by 6 to get

(1/2)x - 1/3 = 5/6

6*[ (1/2)x - 1/3 ] = 6(5/6)

6*(1/2)x - 6*(1/3) = 6(5/6)

3x - 2 = 5

At this point, the fractions are gone. We can now solve like so

3x-2 = 5

3x-2+2 = 5+2 ... adding 2 to both sides

3x = 7

3x/3 = 7/3 dividing both sides by 3

x = 7/3