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O Level · Mathematics A 4MA1

Linear equations

Revise Linear equations for Mathematics A 4MA1 (O Level) — revision notes, 236 practice questions and instant AI marking.

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Pearson Edexcel International GCSE Mathematics A (4MA1)

Linear equations

The big idea: An equation is a balance: whatever you do to one side you must do to the other. Solving means undoing operations until the unknown stands alone, and you can always check the answer by substituting it back.

Summary — What This Chapter Covers

Solve equations with the unknown on one side or both sides.
Expand brackets first; clear fractions by multiplying every term by the common denominator.
Answers may be negative or fractional; leave them exact unless told to round.
Set up an equation from a context (angles, perimeters, ages), solve it, then answer the question asked.

1. Unknown on One Side or Both Sides

Foundation & Higher

Keep the balance

Do the same operation to both sides. With x on both sides, move the x terms to the side with more x first (this avoids negative coefficients), then deal with the numbers.

Worked Example

Solve 5x + 8 = 12.

Worked Example

Solve 7(x + 3) = 5x − 8.

Practice Question 1

Solve 3(2x − 1) = 2(x + 5) + 3.

2. Equations with Fractions

Foundation & Higher

Clear the denominators first

Multiply every term on both sides by the denominator (or the lowest common multiple of the denominators). Put brackets round numerators with more than one term before multiplying.

Worked Example

Solve (4x + 5)/3 = 2.

Practice Question 2

Solve x/4 + 3 = 7 − x/2.

3. Setting Up Equations

Foundation & Higher

Turn the words into algebra

Write an expression for each quantity in terms of one letter, use a fact (angles in a triangle add to 180°, perimeter is the sum of the sides, a total is given) to make an equation, solve it, then answer the actual question — it may ask for an angle or a length, not just the letter.

Worked Example

The three angles of a triangle are a°, (a + 10)° and (a + 20)°. Find the value of a.

Practice Question 3

A rectangle has length (3x + 2) cm and width (x − 1) cm. Its perimeter is 34 cm. Find the length of the rectangle.

Practice Question 4

Ali is x years old. His sister is 4 years older than Ali. Their father is three times Ali's age. Their ages add up to 64. How old is the father?

4. Harder Fractional Equations

Higher tier

Several fractions with different denominators

Memorise

Balance

Same operation, both sides, every term.

Fractions

Multiply every term by the LCM of the denominators. Bracket the numerators.

Check

Answer the question

Common Mistakes

Multiplying only some terms

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Linear equations

Linear equations

Keep the balance

Clear the denominators first

Turn the words into algebra

Several fractions with different denominators

Balance

Fractions

Check

Answer the question

Past papers that test Linear equations

More Mathematics A topics