- One fraction with x on the bottom
- Cross-multiplying a proportion
- Several terms: the common denominator
- When it becomes a quadratic
- Why a false candidate appears
- Check every candidate
- No solution, zero, or build one
- Shared work: rates add
- Round trips: times add
- Mixtures and records: x on both
- Reject answers the story forbids
- Unlocks after
- Opens up