Question 66963
From the beginning we have
5x-(2x+2) = x+(3x-5)

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

Now that we got rid of those horrible parentheses we can do something with this equation.

Let's start by adding two to both sides:

(5x-2x-2)+2 = (x+3x-5)+2

to get

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

Now let's add the "x" terms

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

Now let's subtract 3x to both sides

3x-3x = (4x-3)-3x
0 = 4x-3-3x
0 = x-3

Now simply add 3 to both sides

0+3 = (x-3)+3
3 = x-3+3
3 = x-0
3=x.  You can see by plugging 3 into the original equation that 3 is the correct answer.

The key to problems like these are to utilize the following equalities
For any numbers a,b, and c, we have
a(b+c) = ab+ac
(a+b)c= ab+ac.

These helped alot when we added "x" terms.  For instance the fact that 2x+6x=8x may not make since to someone first starting out with algebra.  But, to look at it another way and utilizing the above formulas we see

2x+6x = (2+6)x = 8x

When we had 5x-(2x+2), let's first "drop" the 5x and look at just -(2x+2).  Well, this is just -1(2x+2).  So, using the above formulas, we have -2x-2 when we multiply out the (-1).  That is how I got 5x-(2x+2) = 5x-2x-2.  

I hope this helps!