Solve $\dfrac{x+5}{4}=\dfrac{2x-1}{3}$.

Cross-multiply: $3(x+5)=4(2x-1)$. $3x+15=8x-4$, so $19=5x$. $x=\tfrac{19}{5}=3.8$. Answer: $x=3.8$

Edexcel IGCSE 4MA1 Linear Equations: Exam Questions & Answers

Q: How do I check my answer to a linear equation?

Substitute it into both sides of the original equation. If both sides give the same number, it is right. For 6(x − 2) = 2(x + 8) with x = 7, both sides are 30.

Q: When do I reverse the inequality sign?

Only when you multiply or divide both sides by a negative number. Adding, subtracting, or multiplying and dividing by a positive number leave the sign as it is.

Q: Can I use a calculator for linear equations in 4MA1?

Yes. A calculator may be used in all four 4MA1 papers, so both Higher papers (1H and 2H) allow one. Most marks are for the method you write down, so show your working.

Q: How long are the 4MA1 Higher papers?

Papers 1H and 2H are 2 hours each and 100 marks each, worth 50% each. Each tier has its own formulae sheet in the exam.

Edexcel IGCSE 4MA1 Linear Equations: exam questions and answers, notes and worked examples

Updated October 2026 · By Pete Bromfield

To solve a linear equation, do the same to both sides until the unknown is on its own: expand any brackets, collect the unknown on one side, then divide.

4 x + 3 = x + 15

gives

3 x = 12

, so

x = 4

. With fractions, multiply every term by the common denominator first, and check your answer by substituting it back in.

Unit 3: Equations & Sequences

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Start with one question on linear equations. Stuck? Take a hint. No sign-in needed.

Solve

6 x - 5 = 2 x + 15

Choose your answer · keys 1–4

x = - 5

x = \frac{5}{2}

x = \frac{10}{3}

x = 5

Linear Equations notes

One-step and two-step equations

Undo the operations in reverse order. $3 x - 4 = 17$ : add 4, then divide by 3, so $x = 7$ . $\frac{x}{5} + 2 = 6$ : subtract 2, then multiply by 5, so $x = 20$ .

Brackets and unknowns on both sides

Expand first, then move the smaller $x$ term so the coefficient stays positive. $3 (2 x + 1) = 4 x + 11$ becomes $6 x + 3 = 4 x + 11$ , so $2 x = 8$ and $x = 4$ .

Equations with fractions

Multiply every term by the lowest common denominator. For $\frac{x + 1}{3} - \frac{x - 2}{4} = 2$ , multiply by 12: $4 (x + 1) - 3 (x - 2) = 24$ , so $x + 10 = 24$ and $x = 14$ .

Forming equations

Call the unknown $x$ , write each quantity in terms of it, then use the fact the question gives you: a total, a perimeter or an angle sum. A rectangle with length $2 x + 3$ , width $x$ and perimeter 36 gives $2 (3 x + 3) = 36$ , so $x = 5$ .

Linear inequalities

Solve them like equations, but reverse the sign if you multiply or divide by a negative number: $5 - 2 x \leq 11$ gives $- 2 x \leq 6$ , so $x \geq - 3$ . For $- 3 < 2 x + 1 \leq 9$ , do the same to all three parts: $- 2 < x \leq 4$ , so the integers that satisfy it are $- 1, 0, 1, 2, 3, 4$ .

Key formulas

Inequalities: multiplying or dividing by a negative number reverses the sign Learn it

Learn it = not printed on the 4MA1 Higher formulae sheet, so learn it by heart. The whole 4MA1 formula sheet (free PDF) → · 4MA1 formulas to learn

Linear Equations worked examples

Worked example 1: Brackets on both sides

Solve $6 (x - 2) = 2 (x + 8)$ .

Solution

Expand: $6 x - 12 = 2 x + 16$ .
$4 x = 28$ , so $x = 7$ .

3 steps · 1 to fill in

Tip: Collect x terms on the side with more x.

Worked example 2: Equation with fractions

Solve $\frac{x + 5}{4} = \frac{2 x - 1}{3}$ .

Solution

Cross-multiply: $3 (x + 5) = 4 (2 x - 1)$ .
$3 x + 15 = 8 x - 4$ , so $19 = 5 x$ .
$x = \frac{19}{5} = 3.8$ .

4 steps · 1 to fill in

Tip: Brackets keep the whole numerator together.

Worked example 3: Forming an equation

A triangle has sides $x$ , $x + 4$ and $2 x - 1$ cm. Its perimeter is 31 cm. Find $x$ .

Solution

$x + (x + 4) + (2 x - 1) = 31$ .
$4 x + 3 = 31$ , so $x = 7$ .

3 steps · 1 to fill in

Tip: Define the unknown and write the equation in words first.

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Common linear equations mistakes

Doing different things to each side. Whatever you do to one side, do to the whole of the other side: every term.
Expanding with a negative. $- 3 (x - 2) = - 3 x + 6$ , not $- 3 x - 6$ : a negative times a negative is positive.
Multiplying only the fractions. When you clear fractions, multiply every term by the common denominator, including the whole numbers on the other side.
Not reversing the inequality. Dividing $- 2 x \leq 6$ by $- 2$ gives $x \geq - 3$ . Keeping $\leq$ gives the wrong half of the number line.

Where students lose marks across 4MA1, from the examiner reports →

Linear Equations FAQ

How do I check my answer to a linear equation?

Substitute it into both sides of the original equation. If both sides give the same number, it is right. For 6(x − 2) = 2(x + 8) with x = 7, both sides are 30.

When do I reverse the inequality sign?

Only when you multiply or divide both sides by a negative number. Adding, subtracting, or multiplying and dividing by a positive number leave the sign as it is.

Can I use a calculator for linear equations in 4MA1?

Yes. A calculator may be used in all four 4MA1 papers, so both Higher papers (1H and 2H) allow one. Most marks are for the method you write down, so show your working.

How long are the 4MA1 Higher papers?

Papers 1H and 2H are 2 hours each and 100 marks each, worth 50% each. Each tier has its own formulae sheet in the exam.

Practise linear equations with your progress saved

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Edexcel IGCSE 4MA1 Linear Equations: exam questions and answers, notes and worked examples

Try it first

Linear Equations notes

One-step and two-step equations

Brackets and unknowns on both sides

Equations with fractions

Forming equations

Linear inequalities

Key formulas

Linear Equations worked examples

Worked example 1: Brackets on both sides

Solution

Worked example 2: Equation with fractions

Solution

Worked example 3: Forming an equation

Solution

Common linear equations mistakes

Linear Equations FAQ

Next steps

Practise linear equations with your progress saved

More Unit 3 topics: Equations & Sequences