IGCSE Maths 0580 · Common mistakes
Common mistakes when solving equations in IGCSE Maths
Updated · by the Fahmazing team
Solving equations is the skill most other topics depend on. A single sign slip early in a question can cost every mark that follows. These are the mistakes we see most often, and how to fix them.
1. Doing something to only one side
Whatever you do to one side you must do to the other. Write the step on both sides every time.
Solve 3x + 5 = 20
✗ Wrong: 3x = 20, so x = 6.67
✓ Right: 3x + 5 − 5 = 20 − 5, so 3x = 15, so x = 5
Free lesson: Equations
2. Undoing with the wrong operation
3x means 3 × x. To undo multiplying, divide. Taking away 3 is the classic slip.
Solve 3x = 12
✗ Wrong: x = 12 − 3 = 9
✓ Right: x = 12 ÷ 3 = 4
Free lesson: Equations
3. Moving a term without changing its sign
When a term crosses the = sign it flips from + to − or from − to +. Safer still: add or subtract the same thing on both sides.
Solve 5x − 4 = 2x + 11
✗ Wrong: 5x + 2x = 11 − 4, so 7x = 7, so x = 1
✓ Right: 5x − 2x = 11 + 4, so 3x = 15, so x = 5. Check: 25 − 4 = 21 and 10 + 11 = 21.
Free lesson: Equations
4. Simultaneous equations: forgetting that subtracting flips every sign
When you subtract one equation from another, every term in the second equation changes sign. Then find both unknowns and check them in both equations.
Solve 3x + 2y = 13 and 3x − y = 7
✗ Wrong: Subtract: 2y − y = y, so y = 6
✓ Right: Subtract: 2y − (−y) = 3y and 13 − 7 = 6, so y = 2. Then 3x − 2 = 7, so x = 3. Check: 9 + 4 = 13.
Free lesson: Simultaneous equations
5. Quadratics: copying the sign out of the bracket
If (x + 4) = 0 then x = −4. The sign flips when you solve each bracket.
Solve x² + x − 12 = 0
✗ Wrong: (x + 4)(x − 3) = 0, so x = 4 or x = −3
✓ Right: (x + 4)(x − 3) = 0, so x = −4 or x = 3
Free lesson: Quadratic equations
6. Dividing both sides by x
Never divide an equation by x. You lose the solution x = 0. Factorise x out instead.
Solve x² = 5x
✗ Wrong: Divide by x: x = 5
✓ Right: x² − 5x = 0, so x(x − 5) = 0, so x = 0 or x = 5
Free lesson: Quadratic equations
7. The quadratic formula: dividing only part of the top
The whole of −b ± √(b² − 4ac) is divided by 2a. Watch the sign of −4ac when c is negative, and use brackets on your calculator.
Solve 2x² + 3x − 4 = 0 (answers to 3 s.f.)
✗ Wrong: b² − 4ac = 9 − 32 = −23, so no solutions
✓ Right: b² − 4ac = 9 − 4 × 2 × (−4) = 9 + 32 = 41. x = (−3 ± √41) ÷ 4, so x = 0.851 or x = −2.35
Free lesson: Quadratic equations
Questions students ask
How can I check my answer to an equation?
Substitute it back into the original equation. If both sides give the same value, it is correct. For simultaneous equations, check both equations.
When should I use the quadratic formula instead of factorising?
If the question asks for answers to a number of decimal places or significant figures, the quadratic will not factorise, so use the formula or completing the square.
Why do I lose marks on simultaneous equations when my method is right?
Usually from a sign error when subtracting, or from giving only one unknown. "Solve" means find both x and y.