Q:  Solve for x:  x/2- 1+x/5 = -1/2

A:  The first thing I like to do is get rid of denominators (fractions) if possible!  In order to do this, I look at all of the denominators: 2, 5, 2.  So really, the two denominators are 2 & 5 (repeats don’t matter).  What number do both 2 & 5 go into?  10!  Therefore, I am going to multiply every part of the equation by 10.

x/2- 1+x/5 = -1/2  [now multiply each part by 10]

10(x/2)- (10)1+(10)x/5 = -1/2(10)

10x/2 – 10 + 10x/5 = -5  [I just reduced a bit and combined]

Keep reducing to get:

5x – 10 + 2x = -5

And combine:

7x – 10 = -5

And solve!

7x = 5

x = 5/7