He didn't explain anything.  Let's do it step by step.

5x-3 = 3x+4

We take care of the LEFT SIDE FIRST, 5x-3

We want to get rid of all terms on the LEFT that do not contain 
the letter x, and keep all the terms that have the letter x.  
So we want to keep the 5x on the left and get rid of the -3 on
the left.

To get rid of the -3 on the left we add +3 to both sides, 
like this:

5x-3 = 3x+4
  +3     +3
-----------
5x   = 3x+7

Now we take care of the RIGHT SIDE, 3x+7.

It's the other way around on the right side.
We want to get rid of all terms on the RIGHT that contain 
the letter x, and keep all the terms that do not contain
the letter x.  So we want to keep the +7 on the right and 
get rid of the 3x on the right.

To get rid of the 3x we add -3x to both sides, like this:

 5x = 3x+7
-3x  -3x
-----------
 2x =    7

Now we want to get rid of the 2 coefficient of x.  To do that
we DIVIDE both sides by 2.  That is we put each side OVER 2,
like this:

 2x     7
———— = ———
  2     2

Then we can cancel the 2's, like this:



And we end up with



So the solution is 

We check by substituting in the original equation:

5x-3 = 3x+4
5-3 = 3+4
-3 = +4
We write 3 as  and 4 as 
 = 
 = 

Both sides are equal, so the solution is correct.
[It was harder to check than to solve].

Edwin