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.

Step-by-Step:

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 times x minus 3 times 4

3(x − 4) = 3 × x − 3 × 4

3x − 12

We have expanded both sets of brackets:

3

Collect like terms.
  • 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

The slider below shows another real example of how to solve an equation with two sets of brackets.