IGCSE Maths / Algebraic equations
Equations with brackets revision notes
Edexcel International GCSE Maths (4MA1), chapter 5: Algebraic equations, specification point 2.4a-f. Free lesson.
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To solve a linear equation with brackets, expand first, then collect terms and isolate the unknown. Checking by substituting your answer can catch errors.
How to solve equations with brackets
A bracket is an extra step in an otherwise ordinary equation. Expand it first because you cannot collect terms while they are still inside a bracket. Keep the equation balanced by doing the same operation to both sides. Expand any brackets. Collect like terms on each side. Gather the letters on one side and the numbers on the other, then divide to find the unknown.
Expand and solve a single bracket
The number outside a bracket multiplies every term inside it. Once expanded, solve the resulting equation by undoing the operations in reverse order.
Solve when both sides have brackets
Expand both sides first. Then move the terms containing the unknown together. In this example, taking 2x off both sides leaves the unknown terms on the right.
A minus outside the bracket changes both signs
When a negative number multiplies a bracket, multiply it by every term inside. A negative multiplied by a negative gives a positive, so the second term changes sign too. 12 − 2(x − 3) = 12 − 2x + 6 = 18 − 2x The incorrect expansion 12 − 2x − 6 loses the positive sign on the second term.
When you can divide before expanding
If one whole side is a single bracket multiplied by a number, divide both sides by that number. This is quicker than expanding. It does not work if another term is added on that side, so expand in that case. 3(x + 4) = 21 Divide both sides by 3 to get x + 4 = 7.
Check your answer by substituting
Put your answer back into the original equation. Both sides should have the same value. This helps catch slips in expanding or rearranging. For x = 3 in 3(x + 4) = 21: 3(3 + 4) = 21. For x = 7 in 2(x + 5) = 4(x − 1): 2 × 12 = 24 and 4 × 6 = 24.