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Solving Linear Equations for IGCSE Maths

Finding the value of x in equations with one unknown. This subtopic is part of Algebra in the Cambridge IGCSE Mathematics 0580 syllabus (both Core and Extended tiers). Understanding solving linear equ

What You Need to Know

Finding the value of x in equations with one unknown. This subtopic is part of Algebra in the Cambridge IGCSE Mathematics 0580 syllabus (both Core and Extended tiers). Understanding solving linear equations is essential for achieving a strong grade in your IGCSE Maths exam.

Understanding Solving Linear Equations

A linear equation contains the unknown to the power 1 only. The goal is to isolate x using inverse operations: undo addition/subtraction first, then multiplication/division. IGCSE 0580 tests: equations with brackets, unknowns on both sides, fractional equations, and forming equations from context. Linear equations appear on every Core and Extended paper and are also used inside multi-step questions.

Step-by-Step Method

  1. 1

    Expand any brackets

    Expand before moving terms. 3(2x−1) = 5 becomes 6x − 3 = 5 before anything else.

  2. 2

    Move all x-terms to one side

    Subtract or add to collect x-terms on the left: 6x − 3 = 5 → 6x = 8.

  3. 3

    Move all numbers to the other side

    Add or subtract to leave only numbers on the right.

  4. 4

    Divide to find x

    Divide both sides by the coefficient of x. If the coefficient is negative, the answer is negative.

  5. 5

    Check by substituting back

    Replace x with your answer in the original equation. Both sides should be equal.

Worked Example

Question

Solve 5(x − 2) = 3x + 8.

Solution

Step 1: Expand. 5x − 10 = 3x + 8 Step 2: Move x-terms to the left. 5x − 3x = 8 + 10 2x = 18 Step 3: Divide. x = 9 Check: 5(9−2) = 5×7 = 35. 3(9)+8 = 27+8 = 35. ✓ Answer: x = 9

Exam Tips for Solving Linear Equations

  • Expand brackets before moving terms — trying to do both at once causes sign errors.
  • When moving a term across the equals sign, its sign changes: +3 on the right becomes −3 on the left.
  • For fractional equations, find the LCM of the denominators and multiply through first to clear fractions.
  • Always check your answer by substituting back — if the two sides are equal, you have the right answer.

Practice Questions

Q1: Solve 4x + 7 = 2x − 3.

Show hint

Move x-terms: 4x − 2x = −3 − 7. Combine: 2x = −10.

Q2: Solve (x+2)/3 = (2x−1)/5.

Show hint

Multiply both sides by 15 (LCM): 5(x+2) = 3(2x−1). Expand, then solve.

Q3: A number is multiplied by 4, then 7 is subtracted. The result equals twice the original number plus 5. Find the number.

Show hint

Let the number be n. Equation: 4n − 7 = 2n + 5.

Frequently Asked Questions

What is solving linear equations in IGCSE Maths?

Finding the value of x in equations with one unknown.

Is solving linear equations in the Core or Extended syllabus?

Solving Linear Equations is part of the Core and Extended syllabus for IGCSE Mathematics 0580.

How do I revise solving linear equations effectively?

Start with the revision notes to understand key concepts, then work through the worked examples step by step. Finally, practise past paper questions under timed conditions. Teacher Rig recommends spending focused revision sessions on solving linear equations rather than trying to cover everything at once.

Need Help with Solving Linear Equations?

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