- Solve .[3]
Loading...
An equation is a balance: whatever you do to one side, you must do to the other. Solving a linear equation — one where the unknown is not squared or multiplied by itself — means undoing the operations around the unknown, step by step, until it stands alone. The skill is simple to state and worth a lot of marks, because equations appear inside almost every other topic.
The big picture
Every step in solving an equation keeps both sides equal while making the equation simpler. Inverse operations undo what has been done to the unknown, in reverse order: if was multiplied by 3 and then had 5 added, subtract 5 first and then divide by 3.
Edexcel frequently hides a linear equation inside a context — angles in a shape, ages, costs, perimeters — so forming the equation correctly from words or a diagram is often the harder part.
What you'll learn
Undo operations in the reverse order to the one in which they were applied. For : add 7 to get , then divide by 4 to get .
Write each step on a new line so the working can be followed and checked.
Check by substituting back: ✓.
Solve .
Expand any brackets first.
If the unknown appears on both sides, collect the unknown terms on the side where the coefficient stays positive, and the numbers on the other.
Answers can be negative or fractional — do not assume a whole number.
Solve .
Tip — Moving from the right to the left means subtracting from both sides. Say "subtract" rather than "move over and change sign" — it keeps the logic clear.
Multiply every term on both sides by the lowest common multiple of the denominators. This clears all the fractions at once.
Put brackets around numerators with more than one term before multiplying, to keep signs correct.
Solve .
A fraction like 13/3 is fine.
Multiplying by 12 gives , and the minus sign in front then applies to both terms: . Without the bracket, the would wrongly become .
Choose a letter for the unknown and say what it represents. Write the other quantities in terms of it, then use a fact from the question — a total, a perimeter, an angle sum — to form an equation.
After solving, answer the question that was actually asked.
A rectangle has length cm and width cm. Its perimeter is 38 cm. Find .
Tip — Check your answer in the original context: here the angles do sum to .
Think like an examiner
Solving equations
Watch out for these
Stretch yourself
Amira is three times as old as her son. In 12 years’ time she will be twice as old as he is. How old is each of them now?
Hint — Let the son be years old now. Write both ages in 12 years, then use "twice as old".
Questions students ask
Key takeaways
Exam-style questions
3 original questions · 10 marks, written to match the style and mark allocation of the real papers. Work on paper, then open the mark scheme and tick the marks you earned — method marks count even if the final answer slips.
An isosceles triangle has two equal sides of length cm and cm. Its third side is cm.
Unlimited practice
A new question every time, marked instantly, with a full worked solution. Aim for a streak of five, then move up a level.
Generating a question…
Test yourself
Ready to practise Linear Equations? Pick a mode and earn XP & Dobloons.
Real past-paper questions on Linear Equations, marked mark-by-mark. How you do feeds straight into your weak-topic list, so your revision keeps targeting what actually needs work.