Mathematics · Grades 8–11
Find the mistake: algebra · revision card
Apply the same valid operation to both sides and respect restrictions such as division by zero.
Keep these ideas clear
Keep equations balanced
Apply the same valid operation to both sides and respect restrictions such as division by zero.
Check by substitution
Substituting a proposed solution into the original equation can expose an error.
Two useful examples
A pupil expands 3(x + 4) as 3x + 4. Correct it.
3x + 12. The factor 3 multiplies both terms.
3x + 12. The factor 3 multiplies both terms.
A pupil says (x + 5)² = x² + 25. What is missing?
The middle term 10x is missing: (x + 5)² = x² + 10x + 25.
The middle term 10x is missing: (x + 5)² = x² + 10x + 25.
Explain it without looking
- Why check a solution in the original equation rather than only a transformed one?
Further reading and review references
These are reference links, not copied exercises, institutional endorsement or proof of independent review.
Learning preview · teacher review required. Grade bands are approximate, not official curriculum alignment.