Strange Solutions

No solution, or infinitely many

An interactive lesson with 8 steps, about 7 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• If $x$ cancels and leaves a false statement (like $3 = 5$), there's no solution.
• If it leaves a true statement (like $2 = 2$), every $x$ is a solution: an identity.
• $x = 0$ is a real solution. Never divide by something that could be zero.

Steps

1. Something’s off
2. When the unknowns vanish
3. Which kind?
4. And this one?
5. The vanishing solution
6. A balance on a graph
7. One, none or infinitely many
8. Make it impossible