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Solving Equations with Brackets

(KS3, Year 7)

Let's start with a test!

The Test

Here is a -question, multi-choice test for the "Solving Equations with Brackets" lesson. The pass mark is 90%. Don't worry! All the information you need to pass is in the lesson section under the test.

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The Lesson

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

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.solve_equation_with_brackets_step_1

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.solve_equation_with_brackets_step_2
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.

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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This page was written by Stephen Clarke.

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