IGCSE · MATHEMATICS · STUDY GUIDE
A more reliable way to check an algebra answer.
A tidy-looking algebra solution can still be incorrect. The strongest habit is to verify that the final value works in the original problem—not just in the final line of your working.
BY Mohammed Ehab ElNomany
STEP BY STEP
A practical study method.
1. Start by preserving the original problem
Write the exact equation, including brackets and fractions. If you rearrange an equation, keep the equals sign balanced. Make one operation per line; it becomes easier to find the first incorrect step. If the problem includes a domain restriction (for example, a denominator that must not equal zero), record it before simplifying.
2. Worked example: solve and verify
Suppose the question is 3(x − 2) = 2x + 5. Expand the left side to get 3x − 6 = 2x + 5. Subtract 2x from both sides: x − 6 = 5. Add 6: x = 11. Now substitute x = 11 into the original equation: 3(11 − 2) = 27 and 2(11) + 5 = 27. Both sides match, so 11 is a solution.
3. Watch for restrictions and extraneous roots
A check matters even more when you square both sides or multiply by an expression containing the unknown: either operation can introduce invalid candidates or hide a forbidden value. For instance, x² = 9 gives x = 3 or x = −3. If a previous line required x ≥ 0, only 3 remains valid. If a denominator is x − 2, x = 2 is not permitted.
4. A five-question self-check
Ask: (1) Did I copy the signs correctly? (2) Did I distribute every bracket term? (3) Did I do the same operation to both sides? (4) Does my proposed answer satisfy the original equation? (5) Have I communicated the final answer and any necessary units or restrictions clearly? This routine is useful for homework review and timed past-paper practice.
5. Make feedback specific
When you discover an error, label its cause: sign error, bracket expansion, incorrect inverse operation, forgotten second root or misreading the question. Then solve a related problem without looking at the original worked solution. This checks whether the underlying misconception has changed, not merely whether you can copy the correction.
PERSONAL SUPPORT
Apply the method to your own course.
Tell me your level, current topic and learning goal. For a learner under 18, a parent or guardian should make contact. Lessons are primarily online; any in-person request in Egypt is considered case by case.