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Solving Two-Step Equations with Positive Integers - Printable Math Worksheets 7th Grade - Wayground

Solving Two-Step Equations with Positive Integers

Anthony Clark

Created by Anthony Clark

20 questions

7th Grade

Math

Solving Two-Step Equations with Positive Integers is a Grade 7 mathematics worksheet that builds fluency with solving one-variable linear equations using inverse operations. Students isolate the variable by undoing addition or subtraction and then multiplication or division, working with equations that include positive and negative integers, coefficients, and constants. The worksheet also includes an item in which students identify an equation from a model. This free printable worksheet includes 20 questions: 13 multiple-choice items, 3 fill-in-the-blank items, and 4 math-response problems. The varied formats ask students to select correct solutions, explain or apply the first step, write answers in equivalent forms, and show solutions to equations such as 5u − 6 = −41 and −28 = 2 + 5w. It is suitable for Grade 7 instruction, independent practice, review, or formative assessment, and includes a complete answer key for efficient checking.

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Solving Two-Step Equations with Positive Integers

Total questions: 20

Name
Class
Date
1.

2y + 10 = 28

a)

y = 9

b)

y = 56

c)

y = 28

d)

y = 10

2.

In the equation

x + 7 = 12

7 is being added to the variable, x.
How should you show your work to isolate the variable and solve the equation?

a)

Subtract 7 from both sides. The solution is x = 5.

b)

Add 7 to both sides.

The solution is x = 19.

c)

Multiply both sides by 7 The solution is x = 84.

3.

2x + 6 = 12

(a)  

4.

26 = 5a + 1

a)

a= 5 4∕5

b)

a= no solution

c)

a= 0

d)

a= 5

5.

Solve for u.

5u - 6 = -41

6.

Solve for w.

-28 = 2 + 5w

7.

Solve for y.

16 = 5y + 6

8.

Solve for w.

2w + 6 = 14

9.

4x + 7 = 23

a)

x = 16

b)

x = 4

c)

x = 9

d)

x = 12

10.

3c + 5 = 23

a)

c = 3

b)

c = 6

c)

c = 7

d)

c = 18

11.

4y + 1 = 13

a)

4

b)

7

c)

3

d)

2

12.
Write the equation for the model.

Write the equation for the model.

a)

3x+6=-9

b)

-3x-6=9

c)

3x+6=9

d)

3x-6=-9

13.

3x + 2 = 44


x = (a)  

14.

8 + 6x = 56


x = (a)  

15.

-3x + 33 = -12

a)

x = 13

b)

x = 14

c)

x = 15

d)

x = 16

16.

7x + 9 = 58

a)

x = 6

b)

x = 7

c)

x = 8

d)

x = 9

17.

What was done to solve the equation?

a)

add 8 to both sides, then divide both sides by 5

b)

add 8 to both sides, then divide both sides by 40

c)

subtract 8 from both sides, then divide both sides by 5

d)

subtract 8 from both sides, then multiply both sides by 5

18.

The steps in solving 5b - 6 = 24 are: 

a)

Add 6 to both sides and divide both sides by 5

b)

Add 6 to both sides and multiply both sides by 5

c)

Subtract 6 from both sides then multiply both sides by 5

d)

Subtract 6 from both sides then divide both sides by 5

19.

What is the first step to solve this equation:
11 - 3x = 44

a)

Add 3 to both sides

b)

Subtract 11 from both sides

c)

Add 11 to both sides

d)

Divide 3 on both sides.

20.

Solve the following two-step equation

2x - 14 = 34

a)

x = 10

b)

x = 48

c)

x = 40

d)

x = 24

WaygroundAnswer Key

Solving Two-Step Equations with Positive Integers

Total questions: 20

1.
a)

y = 9

2.
a)

Subtract 7 from both sides. The solution is x = 5.

3.
3
4.
d)

a= 5

5.

−7-7

6.

−6-6

7.

22

8.

44

9.
b)

x = 4

10.
b)

c = 6

11.
c)

3

12.
a)

3x+6=-9

13.
14, x=14, x= 14, x = 14, x =14
14.
8, x=8, x= 8, x = 8, x =8
15.
c)

x = 15

16.
b)

x = 7

17.
a)

add 8 to both sides, then divide both sides by 5

18.
a)

Add 6 to both sides and divide both sides by 5

19.
b)

Subtract 11 from both sides

20.
d)

x = 24

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FAQs

What does this worksheet cover, and how does it help students solve two-step equations?

This Grade 7 worksheet practices solving one-variable two-step linear equations by using inverse operations to isolate the variable, including equations with positive and negative integers. Its 20 mixed-format items—13 multiple choice, 3 fill-in-the-blank, and 4 math-response questions—require students to select solutions, identify the correct first step, write answers, solve equations, and connect a model to its equation.

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

Introduce the worksheet by modeling how to undo the constant term first and then the coefficient, writing the same operation on both sides of the equation. Use the item about x + 7 = 12 to discuss why subtracting 7 isolates x, then have students apply the same sequence to the multiple-choice and math-response equations. Ask students to explain how they can check a solution by substituting it back into the original equation.

What mistakes should I watch for when students complete this two-step equations worksheet?

Watch for students performing an operation on only one side, reversing the order without correctly undoing the constant, or dividing by the coefficient before removing the added or subtracted term. In the fill-in-the-blank items, students may also enter only the number without recognizing that the requested value is x. For equations with negative terms, check that students preserve signs when moving from an expression such as −3x + 33 = −12 to the final value.

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

You can assign this worksheet on Wayground as a printable PDF or as a digital quiz. It includes a complete answer key for the 13 multiple-choice, 3 fill-in-the-blank, and 4 math-response items, and printable student work can be graded by scanning it with the Wayground for Teachers app.

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

Use the worksheet’s Advanced Settings to adjust font spacing or font size so the equation steps and response areas are easier to follow. You can also apply a dyslexia-friendly font or translate the worksheet into another language when appropriate for students working through the mixed multiple-choice, fill-in-the-blank, and math-response items.

Where can I find more worksheets like this on Wayground?

Wayground offers a broad collection of free printable worksheets and practice problems across 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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