Two-Step Equations: Year 8 Maths
30 October 2026 · Pi Leo Academy
When an equation contains x, guessing can feel like the quickest option. But a small change in the numbers can make guessing frustrating. A two-step method gives Year 8 students something more useful: a way to find the answer and explain why it works.
This lesson focuses on equations where an unknown is multiplied by a number and then a value is added. The aim is to undo those operations while keeping both sides equal.
Watch the lesson
Watch this Pi Leo Academy lesson on YouTube. Pause whenever you want to try a step yourself.
Think of an equation as a balance
The equals sign says the expressions on its two sides have the same value. In 2x + 3 = 11, “2x” means two lots of x. We need to find the value of x that makes the whole statement true.
Imagine a balanced scale. Taking something away from just one side changes the balance. To preserve equality, apply the same operation to both sides.
Worked example: solve 2x + 3 = 11
- Undo the addition. Subtract 3 from both sides: 2x + 3 − 3 = 11 − 3.
- Simplify: 2x = 8.
- Undo the multiplication. Divide both sides by 2: 2x ÷ 2 = 8 ÷ 2.
- The solution is x = 4.
Now check in the original equation: 2 × 4 + 3 = 8 + 3 = 11. The left side matches the right side, so the solution works.
For these equations, the original steps were “multiply, then add”. We undo them in reverse order: subtract, then divide. That order makes it easier to isolate x without creating unnecessary fractions.
A common mistake: changing only one side
In 4x + 1 = 25, removing the +1 only from the left would give 4x = 25. That changes the equation. Subtract 1 from both sides instead: 4x = 24, then x = 6.
Rather than saying a number “jumps across” the equals sign, name the operation. “Subtract 1 from both sides” explains exactly what happened and helps prevent sign errors later.
The Year 8 linear equations study note offers more practice and also covers related inequalities and graphs. This video concentrates on the equation-solving part.
Pause and try two questions
- Solve 3x + 5 = 11.
- Solve 5x + 7 = 22.
Answer 1: Subtract 5 to get 3x = 6. Divide by 3: x = 2. Check: 3 × 2 + 5 = 11.
Answer 2: Subtract 7 to get 5x = 15. Divide by 5: x = 3. Check: 5 × 3 + 7 = 22.
For a short home practice session, write one operation per line and finish every question with a substitution check. A parent can ask, “What did you do to both sides?” rather than supplying the next step.
Your matching study notes
Use these notes alongside the video to revisit the method and practise at your own pace. Full notes and PDF downloads require an eligible Pi Leo Academy membership and sign-in.
Make algebra practice feel manageable
Keep the same calm routine as the questions change. Subscribe to Pi Leo Academy for more topic notes, worked examples and practice, so your child can review a tricky step and try again. Start with one equation, check it carefully, and build from there.
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