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solving multi-step equations - Printable Math Worksheets 8th Grade - Wayground

solving multi-step equations

Karla Ess

Created by Karla Ess

17 questions

8th Grade

Math

Updated Oct 2026

This Grade 8 mathematics worksheet gives students 17 multiple-choice opportunities to solve multi-step linear equations. Problems require combining like terms, using the distributive property, isolating a variable, and solving equations with variables on both sides. Several items also distinguish between one solution, no solution, and infinitely many solutions, while one question asks students to identify the correct first step and another applies equation solving to a house-cleaning cost comparison. The worksheet supports independent practice, guided review, or a quick check of students’ procedural fluency with multi-step equations. Its multiple-choice format helps teachers identify whether errors come from distributing a negative, combining terms incorrectly, or interpreting the resulting equation incorrectly. This is a free printable worksheet with a complete answer key, suitable for Grade 8 math instruction and assessment.

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solving multi-step equations

Total questions: 17

Name
Class
Date
1.
2x - 3 + 4x = 27
a)
12
b)
4
c)
5
d)
15
2.
2x + 3(5x - 7) = 47
a)
x = 1
b)
x = 2
c)
x = 3
d)
x = 4
3.
3x - x + 4 = 4(2x +1)
a)
no solution
b)
all real numbers (infinite)
c)
x = 6
d)
x = 0
4.
3(3x - 6) = 18
a)
x = 4
b)
x = -4
c)
no solution
d)
all real numbers (infinite)
5.
5x - 14 = 8x + 4
a)
6
b)
-6
c)
-18/13
d)
10/3
6.
4(-8x + 5) = -32x - 26
a)
54
b)
-54
c)
all real numbers (infinite)
d)
no solution
7.
38 + 7k = 8(k + 4)
a)
6
b)
8
c)
-6
d)
1
8.
3x - 7 = 3(x - 3) + 2
a)
one
b)
no solutions
c)
infinite solutions
9.

2x + 1 = 2(x -10)

a)

No Solution

b)

x = 0

c)

all real numbers (infinite)

10.
3x + 15 = 3(x + 5)
a)
No Solution
b)
x = 15
c)
all real numbers (infinite)
11.
Question Image
a)
A
b)
B
c)
C
d)
D
12.
Question Image
a)
A
b)
B
c)
C
d)
D
13.
What is the first step in solving the equation 2a - 4(a - 5) = 10
a)
Add 4 to both sides
b)
Add the 2a and a 
c)
Distribute 4 to a and -5
d)
Distribute -4 to a and -5
14.
Solve the equation:
3x - x + 4 = 4(2x +1)
a)
no solution
b)
infinite solutions
c)
x = 6
d)
x = 0
15.
Question Image
a)
1
b)
0
c)
2
d)
7
16.

Pristine House Cleaners charges $19.85 plus $32 per room. Sparkle House Cleaners charges $61.85 plus $18 per room. Write and solve an equation to find the number of rooms for which the total cost of both house cleaners is the same.

a)

4 rooms

b)

1/3 rooms

c)

3.5 rooms

d)

3 rooms

17.
Solve for x:
4 - 2(x - 3) = 24
a)
- 7
b)
7
c)
14
d)
- 14
WaygroundAnswer Key

solving multi-step equations

Total questions: 17

1.
c) 5
2.
d) x = 4
3.
d) x = 0
4.
a) x = 4
5.
b) -6
6.
d) no solution
7.
a) 6
8.
c) infinite solutions
9.
a)

No Solution

10.
c) all real numbers (infinite)
11.
c) C
12.
b) B
13.
d) Distribute -4 to a and -5
14.
d) x = 0
15.
a) 1
16.
d)

3 rooms

17.
a) - 7

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FAQs

What does this solving multi-step equations worksheet cover?

This Grade 8 worksheet uses 17 multiple-choice questions to practise solving multi-step linear equations. Students combine like terms, apply the distributive property, solve equations with variables on both sides, identify one solution, no solution, or infinitely many solutions, and apply an equation to a real-world cost comparison.

How can I use this worksheet to teach students to solve multi-step equations?

Model a consistent sequence with one of the equations: distribute first, combine like terms, move variable terms and constants, and check the result by substitution. Then use the worksheet’s multiple-choice items to pause at the first-step question and discuss why distributing a negative affects both terms. Finish with the cost-comparison problem to connect symbolic equation solving to a practical situation.

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

Watch for students distributing a factor to only one term, especially when the factor is negative, or combining unlike terms while simplifying. Students may also choose a numerical solution when the variable terms cancel, overlooking whether the remaining statement is true or false and therefore represents infinitely many solutions or no solution. In the word problem, check that they set the two pricing expressions equal before solving.

How do I assign and grade this multi-step equations worksheet?

The worksheet is available as a printable PDF and as a digital quiz on Wayground, and it includes a complete answer key for all 17 multiple-choice questions. You can grade printable submissions by scanning student work with the Wayground for Teachers app. The printable option can also support schools that want to reduce screen time.

How can I differentiate this multi-step equations worksheet for my students?

Use the worksheet’s Advanced Settings to adjust font spacing or font size so the equation steps and multiple-choice options are easier to read. You can also apply a dyslexia-friendly font or translate the worksheet into another language while keeping the multi-step equation practice and solution-type questions intact.

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 help students master essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

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