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Equations With Brackets - Printable Mathematics Worksheets class 12 - Wayground

Equations With Brackets

15 questions

8th Grade

Mathematics

Equations With Brackets is a Grade 8 mathematics worksheet focused on expanding brackets and solving algebraic equations. It contains 15 questions: two multiple-choice items that ask students to expand simple expressions such as 2(3 + a), followed by 13 fill-in-the-blank items requiring students to solve for a variable. Most problems require expansion first, while several also require collecting like terms. The final item extends the skill to algebraic modeling: students write an equation for a short verbal situation, expand the brackets, and solve it. This sequence helps students connect the distributive property with simplifying expressions, isolating variables, and recording solutions in the requested form. The worksheet is a free printable resource for Grade 8 math instruction, independent practice, review, or assessment, and it includes a complete answer key.

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Worksheets

Equations With Brackets

Total questions: 15

Name
Class
Date
1.

2(3 + a) 

a)

6 + 2a

b)

5 + a 

c)

5 + 2a 

d)

6 + a

2.

3(4 + c)

a)

12 + 3c

b)

7 + c 

c)

3 + 3c 

d)

4 + c 

3.

Solve the following equation by expanding the brackets first:
2(5+a)=122(5+a)=12  


*Remember to give your answer in the form a=?



(a)  

4.

Solve the following equation by expanding the brackets first:
3(p−7)=63(p−7)=6  


*Remember to give your answer in the form p=?

(a)  

5.

Solve the following equation by expanding the brackets first:
7(p+7)=1337(p+7)=133  

*Remember to give your answer in the form p=?


(a)  

6.

Solve the following equation by expanding the brackets first:
22=2(b+5)22=2(b+5)  

*Remember to give your answer in the form b=?


(a)  

7.

Solve the following equation by expanding the brackets first:
6(3+2d)=546(3+2d)=54  


(a)  

8.

Solve the following equation by expanding the brackets first:
3(2x−4)=183(2x−4)=18  


(a)  

9.

Solve the following equation by expanding the brackets first:
44=4(3a+8)44=4(3a+8)  


(a)  

10.

Solve the following equation by expanding the brackets first:
3(2q−9)=393(2q−9)=39  


(a)  

11.

Solve the following equation by first expanding the brackets. You will need to simplify the expanded expressions by collecting like terms.
5(4s+4)+4s=445(4s+4)+4s=44  


(a)  

12.

Solve the following equation by first expanding the brackets. You will need to simplify the expanded expressions by collecting like terms.
3(4c−5)+c=503(4c−5)+c=50  


(a)  

13.

Solve the following equation by first expanding the brackets. You will need to simplify the expanded expressions by collecting like terms.
40=4y+6(2y−4)40=4y+6(2y−4)  


(a)  

14.

Solve the following equation by first expanding the brackets. You will need to simplify the expanded expressions by collecting like terms.
40=5t+6(4t−3)40=5t+6(4t−3)  


(a)  

15.

Write an equation to match the problem and then solve it by expanding any brackets.


5 is added to x and then this is doubled, giving a result of 14


*Remember only enter the solution x=?

(a)  

Answer Key

Equations With Brackets

Total questions: 15

1.
a)

6 + 2a

2.
a)

12 + 3c

3.
a=1, 1
4.
p=9, 9
5.
p=12, 12
6.
b=6, 6
7.
d=3, 3
8.
x=5, 5
9.
a=1, 1
10.
q=11, 11
11.
s=1, 1
12.
c=5, 5
13.
y=4, 4
14.
t=2, 2
15.
x=2, 2

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FAQs

What does the Equations With Brackets worksheet cover?

This Grade 8 worksheet uses two multiple-choice expansion questions and 13 fill-in-the-blank problems to practise expanding brackets before solving linear equations. Students also simplify expanded expressions by collecting like terms in several items and write an equation from a verbal problem in the final item, building a connected process from distribution to solving.

How can I use this worksheet to teach expanding brackets and solving equations?

Begin by modelling the distributive property with an expression such as 2(3 + a), showing that the multiplier applies to both terms inside the brackets. Then use the first two multiple-choice items to check expansion before moving to the fill-in-the-blank equations, asking students to explain where collecting like terms is needed. Finish by discussing how the final verbal situation becomes an equation before it is solved.

What mistakes should I watch for on this brackets and equations worksheet?

Watch for students multiplying the outside factor by only the first term instead of every term inside the brackets, such as treating 2(3 + a) as 6 + a rather than 6 + 2a. In the later fill-in-the-blank items, students may skip collecting like terms after expansion, or enter only the numerical solution when the prompt requests a form such as a=1. The final item also checks whether they translate the verbal statement into the correct equation before solving.

How do I assign and grade this Equations With Brackets worksheet?

On Wayground, this worksheet is available as a printable PDF and as a digital quiz, so you can use the same 15-item practice set in either format. It includes a complete answer key, and printable submissions can be graded by scanning student work with the Wayground for Teachers app. The printable version can also support instruction in classrooms reducing screen time.

How can I differentiate the Equations With Brackets worksheet for my students?

Use the worksheet’s Advanced Settings to adjust font spacing or choose a larger font size so the expansion steps, algebraic expressions, and fill-in-the-blank response areas are easier to read. You can also apply a dyslexia-friendly font or translate the worksheet into another language while keeping the multiple-choice and equation-solving format.

Where can I find more worksheets like this on Wayground?

Wayground offers a comprehensive collection of free printable worksheets and practice problems across all subjects, with downloadable PDFs and answer keys to support essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

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