GCSE Maths grade 4 basics · topic 4 of 9

Basic algebra: GCSE Maths grade 4 basics

Simplifying, expanding brackets, solving linear equations and substituting numbers into formulae. These are the algebra marks within reach for almost everyone.

Practise: 12 questions Read the basics first

In plain English

Simplify by collecting like terms: 4a + 3b − a + 2b = 3a + 5b. Letters that are different stay separate.
Expand a bracket by multiplying everything inside it by the term outside: 5(x + 3) = 5x + 15.
Solve an equation by doing the same to both sides until x is on its own. Undo adding with subtracting, and multiplying with dividing.
Substitute by replacing each letter with its number, in brackets, then use BIDMAS.

Worked example

Solve 4x + 5 = 29

Subtract 5 from both sides: 4x = 24
Divide both sides by 4: x = 6
Check: 4 × 6 + 5 = 29 ✓

Answer: x = 6

Most common mistake

Wrong5(x + 3) = 5x + 3

Right5(x + 3) = 5x + 15

The number outside multiplies every term inside the bracket, not just the first one.

Practice questions (12)

Try each one on paper first, then open the worked answer and mark yourself. You don't need a calculator for any of these.

Q1.Simplify 4a + 3b − a + 2b
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1. a terms: 4a − a = 3a
2. b terms: 3b + 2b = 5b
Answer: 3a + 5b
Q2.Simplify 3x × 4y
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1. Numbers: 3 × 4 = 12
2. Letters: x × y = xy
Answer: 12xy
Q3.Expand 5(x + 3)
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1. 5 × x = 5x
2. 5 × 3 = 15
Answer: 5x + 15
Q4.Expand and simplify 2(3x − 1) + 4x
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1. Expand: 6x − 2
2. Add 4x: 6x + 4x − 2 = 10x − 2
Answer: 10x − 2
Q5.Factorise 6x + 9
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1. The highest common factor of 6 and 9 is 3
2. 6x ÷ 3 = 2x and 9 ÷ 3 = 3
Answer: 3(2x + 3)
Q6.Solve x + 7 = 15
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1. Subtract 7 from both sides
2. x = 15 − 7 = 8
Answer: x = 8
Q7.Solve 3x − 4 = 11
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1. Add 4 to both sides: 3x = 15
2. Divide by 3: x = 5
Answer: x = 5
Q8.Solve 5x + 2 = 3x + 10
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1. Subtract 3x from both sides: 2x + 2 = 10
2. Subtract 2: 2x = 8
3. Divide by 2: x = 4
Answer: x = 4
Q9.Solve 4(x − 2) = 20
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1. Divide both sides by 4: x − 2 = 5
2. Add 2: x = 7
Answer: x = 7
Q10.a = 3 and b = −2. Work out the value of 4a + 5b.
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1. 4 × (3) = 12
2. 5 × (−2) = −10
3. 12 + (−10) = 2
Answer: 2
Q11.Use the formula v = u + at to find v when u = 5, a = 3 and t = 4.
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1. v = 5 + 3 × 4
2. Multiply first: 3 × 4 = 12
3. v = 5 + 12 = 17
Answer: v = 17
Q12.x = 4. Work out the value of 2x².
Show worked answer
1. Square first (indices before multiplying): 4² = 16
2. Then 2 × 16 = 32
Answer: 32

Can you do these?

Simplify an expression by collecting like terms
Expand a single bracket and factorise
Solve a linear equation, including with brackets or x on both sides
Substitute numbers into an expression or formula

Tick them off on the printable checklist. Want more? The Core sections of our free algebra notes cover the same maths (they are written for IGCSE, but the basics are the same).