20 carefully designed questions — from fill-in-the-blank proofs to tricky multi-step reasoning. Choose your answer, see instant feedback.
Adding the same number to both sides keeps the inequality direction.
Subtracting the same number from both sides keeps direction.
Multiplying both sides by a positive number: direction stays.
Multiplying both sides by a negative number: direction flips!
k(a−b) = ka − kb · Use when multiplying both sides by k.
a < b → a−b < 0 → k(a−b) < 0 → ka < kb (if k > 0)