Moving Variables

We move one variable term to the other side of the equal sign by doing the inverse operation.
Yes we would have to add 4j to 16j in the problem 16j=12-4j because 4j and 16j are like terms.
Therefore you do have to use the inverse operation. The relationship between subtraction and addition is that addition is the inverse operation of subtraction.Their like brother and sister.
The phrase ''what we do to one side we must do to the other'' relates to a balance scale because
by doing something to one side and doing the same to the other your making both sides equal and
a scale is used to tell whether both sides are the same.