# Solving Equations with Two Sets of Brackets(KS3, Year 8)

## The Lesson

We can solve equations with two sets of brackets. Imagine we wanted to solve the equation shown below. ## How to Solve Equations with Two Sets of Brackets

Solving equations with two sets of brackets is easy.

## Question

Solve 2(x + 1) + 3(x − 4) = 0.

# 1

Expand the first set of brackets on the left-hand side of the equation. 2(x + 1) = 2 × x + 2 × 1 2x + 2
Don't forget: Expand the brackets by multiplying each term inside the brackets with the term outside of it.

# 2

Expand the second set of brackets on the left-hand side of the equation, having replaced the first set of brackets with the result of Step 1. 3(x − 4) = 3 × x − 3 × 4 3x − 12
We have expanded both sets of brackets: # 3

Collect like terms.
• Identify the like terms. The like x terms are 2x and 3x. The like number terms are 2 and −12. • Collect the like x terms and the like number terms together • Add or subtract the like terms together.
2x + 3x = 5x

2 − 12 = − 10 # 4

Solve the equation. 5x − 10 = 0 5x − 10 + 10 = 0 + 10 Add 10 to both sides 5x = 10 5x ÷ 5 = 10 ÷ 5 Divide both sides by 5 x = 2

## Answer:

The solution to 2(x + 1) + 3(x − 4) = 0 is x = 2.

## Lesson Slides

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## See Also

What is an equation? Expanding brackets What is a term? What is a like term? Identifying like terms Collecting like terms