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Solving Two-Step Problems Using One Variable - Printable Math Worksheets 7th Grade - Wayground

Solving Two-Step Problems Using One Variable

Barbara White

Created by Barbara White

20 questions

7th Grade

Math

Solving Two-Step Problems Using One Variable is a Grade 7 mathematics worksheet that develops skill with linear equations in one variable. Its 20 multiple-choice questions ask students to find the value of a variable, identify the correct first step, evaluate equations with positive and negative numbers, and solve equations involving multiplication, addition or subtraction, and division. Examples include equations such as 3c + 5 = 23, -4x + 1 = 21, and x / 2 - 5 = 3. The worksheet also checks whether students understand the purpose of solving an equation and can recognize an incorrect solution. Students must apply inverse operations in sequence and manage signs and coefficients while selecting among answer choices. It is designed for Grade 7 math practice, independent work, review, or a quick check of foundational equation-solving skills. This free printable worksheet includes a complete answer key for efficient teacher review and grading.

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Solving Two-Step Problems Using One Variable

Total questions: 20

Name
Class
Date
1.
3c + 5 = 23
a)
c = 3
b)
c = 6
c)
c = 7
d)
c = 18
2.
4x + 7 = 23
a)
x = 16
b)
x = 4
c)
x = 9
d)
x = 12
3.
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.
4.
Figure out what n equals in this equation:
6n + 4 = -26
a)
n=-6
b)
n= -5
c)
n= 8
d)
n= -4
5.
In the equation 4y +-9 =-36
y = -4
a)
True
b)
 francine
c)
False
6.
The goal of solving two-step equations is to:
a)
francine
b)
Find the coefficient 
c)
Find the value of the variable
7.
5x+4=-6
a)
2
b)
-2
c)
10
d)
15
8.
-4x+1=21
a)
x=120
b)
x=5
c)
x=30
d)
x=-5
9.
Solve each equation for the following variable. 
1.     x - 4 = 12
a)
x = 8
b)
x = 16
c)
x = -8
d)
x = 3
10.
2.     2x + 6 = 14
a)
x = 4
b)
x = 10
c)
x = -4
d)
x = 3
11.
6.    -3x + 5 = -13
a)
x = -5
b)
x = 2
c)
x = -6
d)
x = 6
12.
10.    x / 2  - 5 = 3
a)
x = -2
b)
x = 2
c)
x = 16
d)
x = 8
13.
5x+4=-6
a)
2
b)
-2
c)
10
d)
15
14.
6p - 5 =13
a)
12
b)
15
c)
3
d)
-3
15.
Solve for x:
-30 - 5x = 120
a)
x = 18
b)
x = -18
c)
x = 30
d)
x = -30
16.
15 = 2a + 7
a)
2
b)
4
c)
12
d)
14
17.
Solve for w:
-6w + 1 = -11
a)
2
b)
1.2
c)
12
d)
-2
18.
x/5 - 13 = 20
a)
145
b)
165
c)
180
d)
190
19.
4x + 22 = -34
a)
-14
b)
-22
c)
16
d)
-20
20.
12 = 4 - 4x
a)
10
b)
8
c)
4
d)
2
WaygroundAnswer Key

Solving Two-Step Problems Using One Variable

Total questions: 20

1.
b) c = 6
2.
b) x = 4
3.
b) Subtract 11 from both sides
4.
b) n= -5
5.
c) False
6.
c) Find the value of the variable
7.
b) -2
8.
d) x=-5
9.
b) x = 16
10.
a) x = 4
11.
d) x = 6
12.
c) x = 16
13.
b) -2
14.
c) 3
15.
d) x = -30
16.
b) 4
17.
a) 2
18.
b) 165
19.
a) -14
20.
c) 4

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FAQs

What does this worksheet cover, and how does it help students solve one-variable equations?

This Grade 7 worksheet covers solving one-variable linear equations, especially two-step equations, through 20 multiple-choice questions. Students find variable values, identify the first inverse operation, handle negative coefficients and constants, and solve an equation involving division, such as x / 2 - 5 = 3. These varied items reinforce applying inverse operations in the correct order and checking whether a proposed solution is valid.

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

Introduce the worksheet by modeling how to undo the constant operation first and then isolate the variable, using an equation such as 3c + 5 = 23. Have students explain why each operation is applied to both sides before they work independently through the multiple-choice items. Pause to discuss the first-step question for 11 - 3x = 44 and compare how the strategy changes when the coefficient or constants are negative.

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

Watch for students choosing an operation that does not undo the constant first, especially in items such as 11 - 3x = 44. Students may also lose negative signs when dividing by a negative coefficient, confuse the coefficient with the variable's value, or mishandle the division form x / 2 - 5 = 3. The true-or-false item can reveal whether a student is accepting a proposed value without substituting it back into the equation.

How do I assign and grade this worksheet?

This worksheet is available on Wayground as a printable PDF and as a digital quiz, and it includes a complete answer key for all 20 multiple-choice questions. You can assign the PDF for written practice or use the digital quiz for online responses. Printable submissions can be graded by scanning student work with the Wayground for Teachers app.

How can I differentiate this worksheet for my students?

Use the worksheet's Advanced Settings to adjust font spacing or increase the font size so the equations, answer choices, and negative signs are easier to read. You can also select a dyslexia-friendly font for students who benefit from that format or translate the worksheet into another language while preserving its equation-solving practice.

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

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