Keysha, are you looking for a solution / answer? Right now it's just an equation, so nothing to justify yet...?

You need to move the x's to one side and the numbers to the other. There are always several ways to do this. 

Here's one:
13x - 18 = -5x + 36    [now add 18 on both sides]

13x        = -5x + 54    [now add 5x on both sides]

18x       = 54              [now divide by 18]

  x        = 3 

The answer is that "x" has a certain value that makes this equation true.

If you add 18 to both sides, the equation becomes 13x = -5x + 54.

If you add 5x to both sides, the equation becomes 18x = 54.

If you divided both sides by 18, you find that x = 3.

So, when x = 3, then 13x - 18 = -5x + 36

look how they change the given  equation to.. 

they changed to x=? format. 

so.. basically, solving equation means modification.