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8th Grade Math Equations - Printable Mathematics Worksheets year 8 - Wayground

8th Grade Math Equations

20 questions

8th - 8th Grade

Mathematics

This free Grade 8 math worksheet helps students build essential equation-solving and algebra vocabulary through 20 questions: 19 multiple-choice items and 1 multiple-select item. Students identify absolute value, acute and obtuse angles, the coordinate plane, domain, integers, and the x-axis, then simplify algebraic expressions and select equations that represent real-world situations involving fixed costs and rates. The worksheet also asks students to solve linear equations with integers, decimals, and parentheses, including equations such as 6 − 3a = 21 and −3(f − 8) = 39. Designed for Grade 8 mathematics review, independent practice, homework, or a quick skills check, this worksheet moves from recognizing mathematical terms to applying procedures. The contextual equation items help students translate information about pizzas and bike rentals into algebraic equations, while the final problems reinforce isolating variables, managing signs, distributing multiplication, and checking solutions. It is available as a free printable worksheet with a complete answer key for efficient review and grading.

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Worksheets

8th Grade Math Equations

Total questions: 20

Name
Class
Date
1.

Abigail, Aiden, and David are having a blast playing a thrilling number guessing game. They are trying to figure out how far a number is from zero. Can you guess what this exciting game is called?

a)

acute

b)

absolute value

2.

Aria, Priya, and Noah are on a thrilling adventure to build a magical treehouse in their backyard. They come across a challenge where they need to cut a piece of enchanted wood at an angle that is more than 0 but less than 90 degrees. Can you help them figure out what type of angle they should cut?

a)

straight angle

b)

acute angle

3.

Zoe, Anika, and Kai are embarking on an exciting adventure, playing a game of treasure hunt. They have a map in their hands, which is divided by a horizontal and a vertical number line, intersecting at right angles at their origins. This map is divided into four sections. Can you guess what this type of map is called?

a)

Algebraic expressions

b)

Cube root

c)

Coordinate plane

4.

Imagine Abigail, Harper, and Emma are having a fun baking day! They are helping Mia bake a cake using a recipe that lists all the ingredients they need. This list of ingredients can be compared to which mathematical concept?

a)

slope

b)

domain

5.

Imagine David, Ethan, and Nora are playing a fun game of marbles. David has a bag of marbles. The number of marbles can be a negative number if he owes some to Ethan, zero if he has none, or a positive number if he has some. Nora, being the smart one, is asked to identify what type of numbers are these. Can you help Nora?

a)

decimals

b)

whole numbers

c)

integers

6.

Mason, Avery, and Harper are on a treasure hunt. They stumble upon a map with an angle marked on it. The angle is greater than 90 degrees but less than 180 degrees. Can you help them identify what type of angle this is?

a)

obtuse angle

b)

acute angle

c)

straight angle

7.

Imagine this! Michael, Samuel, and Abigail are on a thrilling adventure, playing a game of treasure hunt. They have a mysterious map in their hands, with the treasure spot marked. If they are eagerly examining the map, which axis do you think would represent the horizontal direction?

a)

origin

b)

x-axis

8.

Mason and Avery are having a friendly math competition. Mason challenges Avery with a problem: 'What is the simplified form of x + 2(x + 3)?'

a)

2x + 8

b)

3x + 6

9.

Hannah, Benjamin, and Arjun are playing a math game. Hannah comes up with a challenge for Benjamin and Arjun. She asks them to simplify the expression 5(1 - y) - 3y. Can you help them out?

a)

-8y + 5

b)

-2y + 5

10.

For the grand school carnival, Rohan, Ethan, and Daniel decided to set up a pizza and soda stall. Daniel, who was in charge of the purchases, spent $12.57 on the sodas and $10.95 for each pizza. If the total amount he spent was $89.22, can you help them figure out how many pizzas did Daniel buy for the stall?

a)

12.57x + 10.95 = 89.22

b)

10.95x + 12.57 = 89.22

11.

Aria, Nora, and Arjun decided to go on a thrilling bike adventure. They rented a bike from the popular Maria's Bike Shop. The rental cost was $40, with a security deposit of $22 and an hourly rate of $6. Can you figure out how many hours they rented the bike for?

a)

6x + 22 = 40

b)

40 - 22x = 6

12.

Given the equation

3x + 11 = 2x - 5

The new equation after isolating the variable on one side and the constant on the other would be...?

a)

5x = -6

b)

5x = -16

c)

x = -16

d)

x = 6

13.
6 - 3a = 21
a)
a= 9
b)
a= -9
c)
a= -5
d)
a= 5
14.
Solve the equation. Check your answer.
-2.5b = 20.5 
a)
8.2
b)
-0.12
c)
0.12
d)
-8.2
15.
-3 ( f - 8 ) = 39
a)
-21
b)
-10.3
c)
-5
d)
5
16.
x - 62 = 123
How should you show your work to isolate the variable and solve the equation?
a)
Add 62 to each side. 
b)
Subtract 62 from each side.
c)
Multiply each side by 62.
d)
Add 123 to each side.
17.
3x + 2(4x - 4) = 3
a)
4
b)
3
c)
2
d)
1
18.
Solve the equation:
3x - x + 2 = 4(2x - 1)
a)
infinite solutions
b)
x = 1
c)
x = -1
d)
no solution
19.

Which equation(s) have x = 5 as a solution?

a)

x + 15 = 20

b)

14x = 70

c)

x - 5 = 10

d)

x - 7.3 = 2.3

e)

x + 2.3 = 7.3

20.
Solve the equation:
7x - 4 = 3 + 8x
a)
x = 7
b)
x = -7
c)
x = 2/7
d)
x = 11
Answer Key

8th Grade Math Equations

Total questions: 20

1.
b)

absolute value

2.
b)

acute angle

3.
c)

Coordinate plane

4.
b)

domain

5.
c)

integers

6.
a)

obtuse angle

7.
b)

x-axis

8.
b)

3x + 6

9.
a)

-8y + 5

10.
b)

10.95x + 12.57 = 89.22

11.
a)

6x + 22 = 40

12.
c)

x = -16

13.
c) a= -5
14.
d) -8.2
15.
c) -5
16.
a) Add 62 to each side. 
17.
d) 1
18.
b) x = 1
19.
a)

x + 15 = 20

, b)

14x = 70

, e)

x + 2.3 = 7.3

20.
b) x = -7

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FAQs

What does this Grade 8 math worksheet cover?

This worksheet combines algebra vocabulary with linear-equation skills in 20 items, including 19 multiple-choice questions and 1 multiple-select question. Students identify terms such as absolute value, coordinate plane, domain, integers, and x-axis; simplify expressions like x + 2(x + 3); choose equations for fixed-cost and rate situations; and solve equations involving integers, decimals, and parentheses.

How can I use this worksheet to teach equation solving and algebra vocabulary?

Use the vocabulary items first to activate students’ understanding of terms such as absolute value, acute and obtuse angles, domain, and coordinate plane. Then have students explain how the pizza and bike-rental scenarios become equations before solving the procedural items, such as 6 − 3a = 21 and −2.5b = 20.5. Ask students to show each inverse operation and check one solution by substitution.

What mistakes should I watch for when students complete this worksheet?

Watch for students confusing the x-axis with the origin, or choosing whole numbers when a situation includes negative, zero, and positive values and therefore describes integers. In the expression and equation items, common errors include failing to distribute a negative sign in −3(f − 8), combining unlike terms, reversing the fixed cost and rate in the pizza or bike equations, and losing the negative sign when dividing.

How do I assign and grade this worksheet?

Wayground provides this worksheet as a printable PDF and as a digital quiz, with a complete answer key for all 20 questions. You can grade digital responses through Wayground and grade printable submissions by scanning student work with the Wayground for Teachers app. The printable format can also support schools that are reducing screen time.

How can I differentiate this equations and algebra vocabulary worksheet?

In the worksheet’s Advanced Settings, adjust font spacing and font size to make the vocabulary choices, algebraic expressions, and multi-step equation items easier to read. You can also select a dyslexia-friendly font or translate the worksheet into another language when that better supports access to the word problems and mathematical directions.

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 mastery of essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

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