By Thread Academy · 28 September 2026 · Mathematics
Algebra mistakes are rarely about intelligence — they are about habits. The same handful of slips costs students marks at every level, from grade 8 through A-level. Here are the big ones, with the correct method shown each time.
1. Sign errors when moving terms
The mistake:
3x + 5 = 20 3x = 20 + 5 ← wrong: the +5 should change sign
The fix — whatever crosses the equals sign changes its sign:
3x + 5 = 20 3x = 20 − 5 3x = 15, so x = 5
Habit: say the sign change out loud as you write it. It sounds silly; it works.
2. Forgetting to multiply every term in brackets
The mistake:
3(x + 4) = 3x + 4 ← the 4 was never multiplied
The fix — the number outside multiplies everything inside:
3(x + 4) = 3x + 12
Watch this one especially with minus signs: −2(x − 5) = −2x + 10, not −2x − 10.
3. Dividing only part of an equation
The mistake:
2x + 6 = 14 x + 6 = 7 ← only the left side was halved correctly...
Actually the error here: dividing the left side by 2 gives x + 3, not x + 6. Both sides, every term:
2x + 6 = 14 x + 3 = 7, so x = 4
4. Cancelling terms instead of factors
The mistake:
(x + 3) / 3 = x ← you cannot cancel the 3s; 3 is not a factor of the numerator
You can only cancel common factors of the whole numerator and denominator:
(3x + 6) / 3 = x + 2 ← 3 is a factor of the entire top, so this is fine
5. Squaring a sum term by term
The mistake:
(x + 2)² = x² + 4 ← the middle term is missing
The fix — expand properly:
(x + 2)² = (x + 2)(x + 2) = x² + 4x + 4
How to use this list
Keep these five on a card while you practise. Before you finish any algebra question, run the checklist: signs, brackets, every term divided, factors only, middle term. Most "careless" errors disappear within two weeks of deliberate checking.
Related lessons
Practise the correct methods in these lessons — every one includes worked examples and a quiz.