Solving Equations with Brackets
(KS3, Year 7)

The Lesson

We can solve equations with brackets. Imagine we wanted to solve the equation shown below.

How to Solve Equations with Brackets

Solving equations with brackets is easy.

Question

Solve 2(x + 1) = 6.
There are two methods for solving the equation with brackets.

Method 1

Solve 2(x + 1) = 6 by expanding the brackets first.

Step-by-Step:

1

Expand the 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

Solve the equation.

2x + 2 = 6
2x + 2 − 2 = 6 − 2Subtract 2 from both sides
2x = 4
2x ÷ 2 = 4 ÷ 2Divide both sides by 2
x = 2

Answer:

The solution to 2(x + 1) = 6 is x = 2.

Lesson Slides

The slider below shows another real example of how to solve an equation with brackets. Open the slider in a new tab

Method 2

Solve 2(x + 1) = 6 by dividing by the number in front of the brackets.

Step-by-Step:

1

Divide both sides by the term in front of the brackets (2).
2(x + 1) ÷ 2 = 6 ÷ 2 x + 1 = 3

2

Solve the equation.
x + 1 = 3
x + 1 − 1 = 3 − 1Subtract 1 from both sides
x = 2

Answer:

The solution to 2(x + 1) = 6 is x = 2. Both methods give the same answer.
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See Also

What is an equation? Expanding brackets What is a term? What is an expression?