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Maths Quiz - Level 5-6 Algebra - Equations with Brackets (Questions)

Solve equations with brackets. Expand, simplify, and balance both sides to find x. Practise distributive law and collecting like terms with clear, step-by-step methods.

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Fascinating Fact:

When there are brackets on both sides, such as 3(x + 2) = 2(x + 5), expand both to get 3x + 6 = 2x + 10, then solve x = 4.

In KS3 Maths, you learn to solve linear equations that contain brackets. Use the distributive law to expand, collect like terms, keep the equation balanced, and check your solution by substitution.

Key Terms

Distributive law: Multiply each term inside the brackets by the number outside, for example 3(x + 2) = 3x + 6.
Expand: Remove brackets by multiplying, then write the expression without brackets.
Collect like terms: Combine terms that have the same variable and power, such as 2x + 5x = 7x.

Frequently Asked Questions (Click to see answers)

How do I solve an equation like 4(x − 3) = 2(x + 5)?

First expand: 4x − 12 = 2x + 10. Move x terms to one side and numbers to the other: 4x − 2x = 10 + 12, so 2x = 22 and x = 11.

What is the quickest way to deal with brackets on both sides?

Expand both sides using the distributive law, collect like terms, then use inverse operations to isolate x. Always simplify step by step to avoid mistakes.

How can I check my solution to a bracket equation?

Substitute your value of x back into the original equation. If both sides give the same number, your solution is correct.

Try These Related Quizzes

1.

3 x a + 4 = 6 is the same as which of the following?

[ ]	3 x a = 6 - 4
[ ]	3 x a = 6 / 4
[ ]	3 x a = 6 + 4
[ ]	3 x a = 6 x 4

2.

3b - 16 + b = 1 is the same as which of the following?

[ ]	4b = 1 - 16
[ ]	4b = 1 / 16
[ ]	4b = 1 + 16
[ ]	4b = 1 x 16

3.

3a + 6 + b = 3a + 5 is the same as which of the following?

[ ]	b = 3a - 3a + 5 - 6
[ ]	b = 3a + 3a + 5 - 6
[ ]	b = 3a - 3a - 5 + 6
[ ]	b = 3a - 3a + 5 + 6

4.

2x - 6 could be written as which of the following?

[ ]	(x - 3)2
[ ]	2(x - 3)
[ ]	Either of the above
[ ]	Neither of the above

5.

If 6a - 5 = 20, which of the following is incorrect?

[ ]	6a = 25
[ ]	a = 25 / 6
[ ]	a = 4¹⁄₆
[ ]	a = 4.25

6.

5(a - 4) is the same as which of the following?

[ ]	5a + 20
[ ]	5a - 20
[ ]	5a - 4
[ ]	5a4

7.

Look at the following equation and choose the correct answer when the brackets have been expanded: 4(a + 3) = 5(b - 8)

[ ]	4a - 12 = 5b - 40
[ ]	4a - 12 = 5b + 40
[ ]	4a + 12 = 5b - 40
[ ]	4a + 12 = 5b + 40

8.

If 4(x - 5) = 10, what is the value of x?

[ ]	5
[ ]	7.5
[ ]	10
[ ]	15

9.

If 16(a + 7) = 128, what is the value of a?

[ ]	1
[ ]	2
[ ]	3
[ ]	4

10.

If 5(x + 2) = -35, what is the value of x?

[ ]	-5
[ ]	-9
[ ]	-10
[ ]	10

You can find more about this topic by visiting BBC Bitesize - Equations

Maths Quiz - Level 5-6 Algebra - Equations with Brackets (Answers)

1.

3 x a + 4 = 6 is the same as which of the following?

[x]	3 x a = 6 - 4
[ ]	3 x a = 6 / 4
[ ]	3 x a = 6 + 4
[ ]	3 x a = 6 x 4

When the 4 crosses the equals sign it changes from + 4 to - 4

2.

3b - 16 + b = 1 is the same as which of the following?

[ ]	4b = 1 - 16
[ ]	4b = 1 / 16
[x]	4b = 1 + 16
[ ]	4b = 1 x 16

When - 16 crosses the equals sign it changes to + 16

3.

3a + 6 + b = 3a + 5 is the same as which of the following?

[x]	b = 3a - 3a + 5 - 6
[ ]	b = 3a + 3a + 5 - 6
[ ]	b = 3a - 3a - 5 + 6
[ ]	b = 3a - 3a + 5 + 6

The correct answer could be further simplified to b = -1

4.

2x - 6 could be written as which of the following?

[ ]	(x - 3)2
[ ]	2(x - 3)
[x]	Either of the above
[ ]	Neither of the above

Basically, 2x - 6 is the same as (x - 3) times 2

5.

If 6a - 5 = 20, which of the following is incorrect?

[ ]	6a = 25
[ ]	a = 25 / 6
[ ]	a = 4¹⁄₆
[x]	a = 4.25

You will often find that you have a term such as 6a and you need to separate the 6 from the a in order to determine the value of a

6.

5(a - 4) is the same as which of the following?

[ ]	5a + 20
[x]	5a - 20
[ ]	5a - 4
[ ]	5a4

Removing brackets this way is referred to as 'expanding the brackets'. In this case the 5 outside of the brackets must be multiplied by BOTH the a and the - 4 that are inside the brackets

7.

Look at the following equation and choose the correct answer when the brackets have been expanded: 4(a + 3) = 5(b - 8)

[ ]	4a - 12 = 5b - 40
[ ]	4a - 12 = 5b + 40
[x]	4a + 12 = 5b - 40
[ ]	4a + 12 = 5b + 40

We're multiplying the values in brackets by the numbers in front of them

8.

If 4(x - 5) = 10, what is the value of x?

[ ]	5
[x]	7.5
[ ]	10
[ ]	15

4x - 20 = 10 and therefore 4x = 30

9.

If 16(a + 7) = 128, what is the value of a?

[x]	1
[ ]	2
[ ]	3
[ ]	4

16a + 112 = 128 and therefore 16a = 16

10.

If 5(x + 2) = -35, what is the value of x?

[ ]	-5
[x]	-9
[ ]	-10
[ ]	10

5 x -7 = -35