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.

What Is Solving Equations with Brackets?

An equation with brackets contains at least one set of parentheses that must be expanded before you can solve it. For example, 3(x + 4) = 21 requires you to expand the bracket to get 3x + 12 = 21, then solve for x.

The usual approach is to expand first, then solve. However, if the number outside the bracket divides neatly into the number on the other side, you can sometimes divide first to remove the bracket in one step. Both methods are valid and give the same answer.

More challenging questions have brackets on both sides of the equation. You expand both brackets, collect x terms on one side and number terms on the other, then solve as normal. These are common on Higher tier papers and in the later questions on Foundation papers.

Key Formulas

Step-by-Step Method

1. Expand all brackets by multiplying each term inside the bracket by the term outside.
2. Simplify each side of the equation by collecting like terms.
3. Move all x terms to one side using addition or subtraction.
4. Move all number terms to the other side.
5. Divide both sides by the coefficient of x to find the solution.

Worked Example 1 — Foundation Level

Question: Solve 4(x + 3) = 28.

Working:

Step 1 — Expand: 4x + 12 = 28.

Step 2 — Subtract 12 from both sides: 4x = 16.

Step 3 — Divide by 4: x = 4.

Answer: x = 4

Worked Example 2 — Higher Level

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

Working:

Step 1 — Expand both sides: 10x - 5 = 3x + 12.

Step 2 — Subtract 3x from both sides: 7x - 5 = 12.

Step 3 — Add 5 to both sides: 7x = 17.

Step 4 — Divide by 7: x = 17/7 = 2 3/7.

Answer: x = 17/7

Worked Example 3 — Exam Style

Question: Solve 2(3x + 1) - 3(x - 4) = 20. (3 marks)

Working:

Step 1 — Expand the first bracket: 6x + 2.

Step 2 — Expand the second bracket (watch the minus sign): -3x + 12.

Step 3 — Combine: 6x + 2 - 3x + 12 = 20, which simplifies to 3x + 14 = 20.

Step 4 — Subtract 14: 3x = 6.

Step 5 — Divide by 3: x = 2.

Answer: x = 2

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."

Practice Questions

Q1 (Foundation): Solve 5(x - 2) = 15.

Q2 (Foundation): Solve 2(3x + 4) = 32.

Q3 (Higher): Solve 4(x + 1) = 2(3x - 5).

Practise solving equations with brackets questions with instant feedback — completely free on GCSEMathsAI.

Related Topics

• Expanding Brackets
• Solving Linear Equations
• Equations with Unknowns on Both Sides

Summary

• Expand all brackets first by multiplying every term inside by the term outside.
• Collect x terms on one side and numbers on the other side.
• Watch sign errors, especially when a negative number multiplies a bracket.
• If there are brackets on both sides, expand both before collecting terms.
• Always check your answer by substituting it back into the original equation.