Maths · KS3 and GCSE · Interactive lesson
Solving equations: keep both sides equal
Use boxes and counters to solve equations. Apply the same operation to both sides, undo a step and check the value of x.
Choose your view
Explore an interactive example, then try the questions at your own pace.
KS3 / GCSE · start with the idea
By the end of this lesson: Solve an equation by doing the same operation to both sides.
The interactive diagram and controls are in Stage 2, “Explore one example”. Read the idea here, then try it next.
- The two sides of an equation have the same value.
- Every x in an equation stands for the same unknown number.
- Keep the sides equal: do the same operation to both sides.
Useful starting points
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What do the words mean?
- Equation
- A statement that two amounts are equal.
- Unknown
- The number we are trying to find; x is its name here.
- Inverse operation
- An operation that undoes another: subtraction undoes addition; division undoes multiplication.
Change the example
This is the lesson example. Your practice question uses its own numbers.
Something to try
Choose an equation. Before each operation, predict what will remain on each side.
Notice what changes
How particle motion works +
Starts paused. Press Play, then add energy to see the warmer particles move faster.
Particles keep the same size. Liquid particles move around; solid particles vibrate around fixed positions. This is a simplified model, with the change in motion exaggerated to make it easier to see.
About the playback +
About this model
Purple boxes stand for the same unknown value. Each dot represents 1. This model uses positive whole-number values and shows equality, rather than the size of real weights.
More about this diagram
Still picture. Play particle motion in Stage 2.
2x + 3 = 11
Still picture of the example from Stage 2. Use the back arrow to change it.
Work through it
Starting example: read the steps below
- Start with 2x + 3 = 11. Both sides have the same value.
- Subtract 3 from both sides: 2x = 8.
- Divide both sides by 2: x = 4.
- Check x = 4 in the original equation. Left = 11; right = 11.
Try on your own
Your turn. No rush.
Question 1
Solve 2x + 3 = 11. What is x?
About these questions
Questions appear in a mixed order. Work at your own pace and stop whenever you like.
These questions use their own numbers, separate from the lesson example. You can stop whenever you like. Answers last for this visit to the page.
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Can you explain why the same operation is needed on both sides?
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Notes for parents and tutors
These lessons cover selected KS3 and GCSE ideas for England; they are not a complete course. The level notes explain where GCSE methods or optional extensions begin. Maurice can help you choose material for your course and exam board.
The content draws on the DfE Maths curriculum, DfE Science curriculum and AQA GCSE Physics specification. Level labels are guidance, not exam-board endorsements. For AQA Radioactivity, calculating net decline as a ratio is Higher-tier work. Net means the overall change; ask Maurice whether this extension is relevant to your course. Explanations and practice were reviewed during development on 21 October 2026; Maurice should check their fit before assigning work.
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