Maths Olympiad · topic 18 of 33 · free

Solving linear equations — Maths Olympiad practice

An equation is a balance. To find x, undo what has been done to it, one step at a time, doing the same thing to both sides. In a multiple-choice paper you can also check each option by putting it back into the equation.

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How to solve it

Balance — “whatever you do to one side, do to the other”

  1. Bring the x terms to one side and the plain numbers to the other (change the sign when you move a term across).
  2. Divide both sides by the number in front of x (or multiply if x is divided).
  3. Check by putting your answer back into the equation.

Use it for: Equations, “think of a number” puzzles and age problems in Class 7–10.

Worked example: If 5x + 3 = 2x + 18, what is x? → 5

  1. Take 2x and 3 from both sides: 3x = 15.
  2. Divide by 3: x = 5.

Check: 5 × 5 + 3 = 28 and 2 × 5 + 18 = 28 ✓

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✓ Written and checked by the TalentJR team · Updated 13 Oct 2026 · How we make our lessons

✏️ Practice

Work it out on paper, then tap the answer you think is right. Stuck? Press “Show me how” to see every step.

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🏁 Topic 18 test

20 questions. Check each answer, then go to the next one. Get 16 or more right to pass.

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🖨️ Linear Equations Worksheet for Maths Olympiad

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