Question

Tucker was asked to solve the equation 5x + 3 = 6x + 1. He did not know if his first step should be to add 5 negative x-tiles, or 1 negative unit tile, to both sides. What advice would you give Tucker to help him decide on his first step? Explain

Answer 1

Both moves are allowed — you must do the same thing to both sides — but pick the one that most quickly cancels a whole type of tile.

Here 5x is on the left and 6x on the right. If you add 5 negative x-tiles (i.e. subtract 5x) to both sides, the x-tiles on the left cancel entirely:
5x + 3 = 6x + 1
(−5x) → 3 = x + 1
then subtract 1 → 2 = x.

If you instead add 1 negative unit tile (subtract 1) first you get
5x + 2 = 6x
then subtract 5x → 2 = x.

Both give x = 2, but it is usually simplest to first do the operation that completely cancels a term (here subtract 5x), and if possible leave the variable positive on the remaining side. This avoids extra steps or fractions.