Keep the equation balanced
Do the same operation to both sides. Aim to get all the -terms on one side and the numbers on the other, then divide.
Brackets and fractions first
Multiply out brackets, and remove fractions by multiplying every term by the denominator, before collecting like terms.
Drawn from real examiner reports.
Not multiplying every term
When multiplying both sides to remove a denominator, some terms get multiplied but not others, or brackets are omitted around a multi-term side.
Reported on the November 2024 Higher Paper 1H (Q3c) and June 2024 Higher Paper 1H (Q6b).
Wrong sign collecting terms
Moving an -term or a number to the other side with the wrong sign while gathering like terms — adding when you should subtract.
Reported on the November 2024 Higher Paper 1H (Q3c).
Dividing only one term
When splitting a side into separate fractions, one term is divided by the denominator but not the other, e.g. writing instead of when splitting .
Reported on the June 2024 Higher Paper 1H (Q6b).
Forgetting brackets on a side
Multiplying by 3 needs a bracket on the right: , not . Every term on the multiplied side gets the multiplier.
(general exam technique)
Stopping before dividing out
Reaching and quoting , or and quoting — the final divide by the coefficient is missed. Divide both sides by the number in front of .
(general exam technique)
Substitute your answer back
Putting your solution back into the original equation confirms both sides are equal — a quick, reliable check.
Show one line per step
Write each balancing step on its own line (subtract, add, divide). Clear working earns method marks and makes a sign slip easy to trace.
Clear fractions early
Multiplying through by the common denominator at the start removes fractions and avoids most sign and division slips later.
Do the same to both sides, aiming to get the -terms on one side and numbers on the other.
What should you do before collecting like terms?
Solve .
