Solving for the variable x boils down to isolating it, so we need to collect all of our x's on one side of the equation and "undo" any operations being performed on it.
First, we'll move the 2 over to the right side ("undoing" the subtraction on the left side by adding 2 to both sides):
(3x-2)+2=x+2
3x=x+2
Next, we'll subtract x from both sides to collect all of the x terms on the left side of the equation:
3x-x=(x+2)-x
2x=2
Finally, "undo" the multiplication being performed on x by dividing both sides of the equation by 2:
(2x)/2=2/2
(2/2)x=2/2
2/2 is, of course, another form of 1, so simplifying, we get:
x=1