How to Solve Equations with Two Sets of Brackets
Solving Equations with Two Sets of Brackets
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.
StepbyStep:
1
Expand the first set of brackets on the lefthand 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 lefthand 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

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
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.