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Two Step Equations Model and Word Problems - Printable Math Worksheets 6th Grade - Wayground

Two Step Equations Model and Word Problems

Tarek Canahuati

Created by Tarek Canahuati

10 questions

6th Grade

Math

Updated Oct 2026

This Grade 6 mathematics worksheet builds fluency with representing and interpreting two-step equations. Students answer 10 multiple-choice questions that ask them to identify equations from visual models, select solutions such as x = 6 or x = -2, recognize the correct first inverse operation, and distinguish expressions such as 2x + 3 = -6 and 2x - 3 = 5. The worksheet also connects equations to practical word problems involving fixed charges and per-unit or per-hour rates. Students choose equations for book-printing costs, plumbing bills, choir fundraising, and car-service charges, reinforcing how a constant amount and a variable rate appear in an equation. This free printable worksheet is designed for Grade 6 math practice, review, or formative assessment and includes a complete answer key for efficient checking.

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Two Step Equations Model and Word Problems

Total questions: 10

Name
Class
Date
1.
What equation is represented by this model?

What equation is represented by this model?

a)

x + 3 = 6

b)

2x + 3 = -6

c)

2x + 2 = 4

d)

x - 3 = 6

2.
What is the solution to the model shown?

What is the solution to the model shown?

a)

x = 3

b)

x = 4

c)

x = -2

d)

x = 6

3.
What is the solution to the model shown?

What is the solution to the model shown?

a)

x = -2

b)

x = 2

c)

x = -4

d)

x = 4

4.
Pizzazz Publications is having some books printed. The printer charges $800 plus $5 per book. What equation could help me find how many books can be printed for $4,000?
a)
800 + 5x = 4000
b)
800x + 5 = 4000
c)
4000 + 5x= 800
d)
800 + 5 = 4000
5.
Mr. Piper's plumbing needed repairs. The plumber charged $98 for parts plus $45 per hour for labor. If the bill totaled $458, how could I find out the hours of labored required?
a)
98x + 45 = 458
b)
98 + 45x = 458
c)
45 + 98 = 458
d)
45x - 98 = 458
6.
The 30 members of a choir are trying to raise $1500 to cover travel costs to a singing camp. They have already raised $600. Which equation would you solve to find the average amount each member can raise in order to meet the goal?
a)
30x + 600 = 1500
b)
30x - 600 = 1500
c)
x + 600 = 1500
d)
30x = 1500
7.
Scott works on cars. He charges $35 for each car plus $7 per hour. Write an equation that represents this scenario if Kylie's car bill was $63.
a)
7x + 35 = 63
b)
7x = 63
c)
7x - 35 = 63
d)
35x + 7 = 63
8.
What is equation for this model?

What is equation for this model?

a)

2x + 3 = 5

b)

2x - 3 = 5

c)

2 - 3 = 5

d)

2 + -3 = 5

9.
What is the equation for this model ?

What is the equation for this model ?

a)

5x + 4 = 15

b)

4x - 5 = 15

c)

4x + 5 = 15

d)

9x = 15

10.
What is the first step to solve this equation?

What is the first step to solve this equation?

a)

add 4 to both sides

b)

divide by 2 on both sides

c)

subtract 10 on both sides

d)

subtract 4 from both sides

WaygroundAnswer Key

Two Step Equations Model and Word Problems

Total questions: 10

1.
b)

2x + 3 = -6

2.
d)

x = 6

3.
a)

x = -2

4.
a) 800 + 5x = 4000
5.
b) 98 + 45x = 458
6.
a) 30x + 600 = 1500
7.
a) 7x + 35 = 63
8.
b)

2x - 3 = 5

9.
b)

4x - 5 = 15

10.
d)

subtract 4 from both sides

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FAQs

What does this two-step equations worksheet cover?

This worksheet covers representing two-step equations from visual models, identifying solutions, choosing the correct first inverse operation, and translating fixed-cost and rate-based word problems into equations. Its 10 multiple-choice items require students to connect models and real-world situations to equations such as 800 + 5x = 4000 and 98 + 45x = 458.

How can I use this worksheet to teach two-step equations?

Begin by modeling how a visual representation shows a coefficient, a constant, and the total, then have students explain why each part belongs in the equation. Use the word problems next to discuss how a fixed fee is combined with a per-book, per-hour, or per-item rate, and finish by asking students to justify the first inverse operation before selecting an answer.

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

Watch for students reversing the coefficient and constant in equations such as 98 + 45x = 458, omitting the fixed charge, or using subtraction when the situation describes an added cost. In the model questions, students may misread negative values or confuse the number of variable groups with the standalone amount; in the final item, check that they choose to subtract 4 from both sides before dividing by 2.

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

Assign it as a printable PDF or as a digital quiz on Wayground, depending on whether students should mark printed choices or respond online. The worksheet includes a complete answer key, and printable submissions can be graded by scanning student work with the Wayground for Teachers app.

How can I differentiate this worksheet for my students?

In the worksheet’s Advanced Settings, adjust font spacing or font size to make the equation models, answer choices, and word problems easier to read. You can also apply a dyslexia-friendly font or translate the worksheet into another language when those options support access to the multiple-choice tasks.

Where can I find more worksheets like this on Wayground?

Wayground offers a comprehensive collection of free printable worksheets and practice problems across subjects, including 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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