Solving Equations with Brackets –

Solving equations with brackets is a key algebra skill in GCSE Maths that combines expanding brackets with solving linear equations. You will meet these on both Foundation and Higher papers, often worth 3 or 4 marks.

§Key definitions

Question:

Solve 4(x + 3) = 28.

Q1 (Foundation):

Solve 5(x - 2) = 15.

Q2 (Foundation):

Solve 2(3x + 4) = 32.

Q3 (Higher):

Solve 4(x + 1) = 2(3x - 5).

§Formulas to memorise

a(bx + c) = abx + ac — expand by multiplying each term inside by the number outside

Worked example

Solve 4(x + 3) = 28.

Working:

⚠ Common mistakes

✗Forgetting to multiply every term inside the bracket. In 3(2x + 5), both the 2x and the 5 must be multiplied by 3 to give 6x + 15, not 6x + 5.
✗Sign errors with a negative multiplier. In -2(x - 3), the result is -2x + 6, not -2x - 6. A negative times a negative gives a positive.
✗Not changing the sign when subtracting a bracket. In expressions like 5 - (x + 2), the bracket expands to 5 - x - 2 = 3 - x.

✦ Exam tips

→Always expand brackets as your first step — do not try to solve with the brackets still in place.
→Check your answer by substituting it back into the original equation, including the brackets.
→If both sides have the same coefficient of x after expanding, all x terms cancel and you may get "no solution" or "infinite solutions."

MMXXVI specification · AQA · Edexcel · OCRgcsemathsai.co.uk/formulas/solving-equations-with-brackets

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