Your book gives you the rules for ax = b and (ax+b)(cx+d) = 0. This lab is where you test them: watch a balance tip step by step, sort equations by how many solutions they hide, catch an AI making a mistake, and see a factored equation decide who wins a gym membership.
The book's rule box says ax=b can land in three families: one solution, no solution, or infinitely many. Click each equation below, then click the bucket where it belongs. You'll know instantly if you're right — the reasoning is what matters, not the guess.
Select a card, then choose its bucket. 0 / 6 sorted.
The book's rule: if A · B = 0, then A = 0 or B = 0. These four puzzles come straight from your Application exercises — factor first if you need to, then type both solutions (in any order, decimals like -1.67 are fine).
An AI assistant was asked to solve (3x − 6)(x + 1) = 0. One line in its answer is wrong. Click the line you think has the mistake, then check your reasoning.
Gym A: $20 sign-up fee + $15 per month. Gym B: $20 flat per month, no sign-up fee. Drag the slider to pick a number of months and watch which gym is cheaper. Somewhere, the two bars will meet exactly — that month is the solution of 20 + 15x = 20x.
Five quick questions mixing everything above. Pick an answer to see feedback right away.