Solving Linear Equations?

[hypnos]

Hi All.
Sorry for asking these questions. I know it's pretty simple for all you guys. Algebra has never been my strong point so I've decided to learn it in my spare time from a book. It's teaching me a lot but every so often I come to something that I don't understand.

The book gives an example of a linear equation and shows the steps involved in solving this equation:

3x    x       5x
--  + --  =  ---    -   3
5      2       4

The L.C.M is 20 so everything can then be multiplied by this figure:

2 12x + 10x = 25x - 60
3 12x + 10x - 25x = -60
4 -3x = -60
5 x = -60 / -3
6  x = 20 (by the law of signs)

I've labelled the steps so that I can reference them now... I get confused at step 3. All the expressions containing the X variable from the right have (as they should be) been moved to the left of the equality sign. On step 2 the expression 25x is a positive number but on step 3 it becomes a negative one. I don't understand why this is so. This is where I'm going wrong when it comes to algebra...I'm getting confused with the signs. I understand these basic rules when it comes to signs:

a+(b+c)=a+b+c
a+(b-c)=a+b-c
a-(b+c)=a-b-c
a-(b-c)=a-b+c

Can you show me where I'm going wrong. I know this is pretty simple but it's been a long time since I've done anything like this but would like to learn it and become pretty good. Guess I have to start somewhere.

Thanks a lot.