transposition

Transposition is a shortcut for a move you already know. When a term crosses the equals sign to the other side, it switches sign: a plus becomes a minus, a minus becomes a plus. It is a quick way to gather the variable terms on one side and the constants on the other.

Underneath, this is not magic — it is just adding or subtracting the same term from both sides, with the bookkeeping done in one stroke. Moving +3 from the left is really subtracting 3 from both sides; the 3 lands on the right as −3.

Two cautions. Transposition flips a sign only for terms added or subtracted across the equals sign; a factor that multiplies the whole side is not “transposed” by sign change but undone by division. And the trick applies to the equals sign, not to anything inside parentheses, which must be expanded first.