This method allows us to add or subtract the same element from both sides of the equation without changing the final result, that is, the outcome of the equation will not be affected by the fact that we have added or subtracted the same element from both sides.
Let's see what the logic of this method is:
José and Isabel, for example, are twin siblings who receive their weekly allowance for the first time.
José and Isabel receive euros each, so at this moment they have exactly euros per person.
After a month, each has received another euros, so now each has euros.
We see that adding euros to the amount each of them had has not affected the equivalence between them: both still have the same amount of money.