Question 1162426
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5x + 3 = 7x - 1

I will show every step, but with practice, you will "move" terms from
one side to the other.

Subtract 5x from each side:
5x + 3 - 5x  = 7x - 1 - 5x

Combine like terms  (on the left 5x-5x = 0x which we just drop completely, on the right 7x-5x = (7-5)x = 2x):
     3       = 2x - 1

Add 1 to each side:
     3 + 1   = 2x - 1 + 1
        
Combine:
         4  = 2x


Divide both sides by 2:
         4/2 = 2x/2   (2x/2 = 1x which we write simply as 'x', next line)    

Simplify:
            2 = x    --->  Ans: x = 2


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With experience, you would either do the whole thing in your head or you might do one or two steps:
          5x + 3 = 7x - 1
               4 = 2x    (added 1 to both sides, also subtracted 5x from both sides)
               2 = x      (divided both sides by 2)


Solving for x/isolating x is based on this simple principle:  if there is an equation, then doing the same valid operation to both sides does not affect that equality.