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Solving One and Two Step Linear Equations - Printable Math Worksheets 7th - 10th Grade - Wayground

Solving One and Two Step Linear Equations

Edric Uy

Created by Edric Uy

20 questions

7th - 10th Grade

Math

Updated Oct 2026

Solving One and Two Step Linear Equations is a Grade 7–10 mathematics worksheet that builds fluency with isolating a variable using inverse operations and maintaining equality on both sides of an equation. Students identify the purpose and basic rules of equation solving, choose the correct first or second step, and solve one- and two-step equations involving integers, fractions, decimals, negative values, and coefficients. The 20-question set includes 2 multiple-select items and 18 multiple-choice items. Equations such as 9 + g = 12, 3p + 7 = 19, 6h = -42, and 3.2e + 2.6 = -23 require students to select appropriate operations, sequence steps correctly, and determine the value that makes each statement true. This free printable worksheet includes a complete answer key for classroom practice, homework, review, or assessment.

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Solving One and Two Step Linear Equations

Total questions: 20

Name
Class
Date
1.

The goal of solving linear equations is to: (Pick 2)

a)

Move the constant

b)

Find the value of the variable that makes the statement true

c)

Find the coefficient

d)

Combine like terms

e)

Get the Variable BY ITSELF!

2.

What are the TWO basic rules for solving algebraic equations? (That means pick 2 answers)

a)

What you do on one side you must do to the other (keep balanced)

b)

Negative signs can be ignored

c)

Always use the opposite/inverse operations to solve

d)

You must start on the left side of the equation

3.

What would be the inverse operation for the problem below?


-8p = 24

a)

Add 8 to both sides

b)

Subtract 24 from both sides

c)

Divide both sides by -8

d)

Divide both sides by 8

4.

9 + g = 12

a)

g = 3

b)

g = 21

c)

g = -3

d)

g = 4/3

5.

What is the FIRST step in solving the following equation?


-15 = -10 + 5w

a)

Subtract 5 from both sides

b)

add 10 to both sides

c)

subtract 10 from both sides

d)

add 15 to both sides

e)

Divide by 5 on both sides

6.

What would be the SECOND step in solving the equation below?

 x5+7 =−12\frac{x}{5}+7\ =-12  

a)

Subtract 7 from both sides

b)

Add 12 to both sides

c)

Multiply by 5 on both sides

d)

Divide by 5 on both sides

7.

What are the steps to solving 5y - 6 = 24?

a)

Add 6 to both sides and then divide both sides by 5

b)

Subtract 6 from both sides then multiply both sides by 5

c)

Add 6 to both sides and multiply both sides by 5

d)

Subtract 6 from both sides then divide both sides by 5

e)

Subtract 5 from both sides then divide both sides by -6

8.

Solve


k - 17 = -21

a)

k = -38

b)

k = 4

c)

k = -4

d)

k = 38

9.

Find the value of h that makes the statement true.


6h = -42

a)

h = -48

b)

h = 7

c)

h = -7

d)

h = -252

e)

h = -36

10.

Solve this equation for n.

 n8=6\frac{n}{8}=6  

a)

n = -3/4

b)

n = 3/4

c)

n = -48

d)

n = 48

11.

Solve this algebraic equation.


3p + 7 = 19

a)

p = -4

b)

p = 9

c)

p = 4

d)

p = 8.67

12.

Solve the following equation for h.

 h5+13=17\frac{h}{5}+13=17  

a)

h = 150

b)

h = 20

c)

h = 6

d)

h = 4/5

13.

Solve the following algebraic equation for e.


3.2e + 2.6 = -23

a)

e = 6.375

b)

e = 8

c)

e = -8

d)

e = -6.375

14.
6 - 3a = 21
a)
a= 9
b)
a= -9
c)
a= -5
d)
a= 5
15.

h + 1.6 = 11

a)

h = 9.4

b)

h = 12.6

c)

h = 12.4

d)

h = 94

16.
Which of the follow represents the CORRECT FIRST STEP to SOLVING this Equation?

Which of the follow represents the CORRECT FIRST STEP to SOLVING this Equation?

a)
Which of the follow represents the CORRECT FIRST STEP to SOLVING this Equation?
b)
Which of the follow represents the CORRECT FIRST STEP to SOLVING this Equation?
c)
Which of the follow represents the CORRECT FIRST STEP to SOLVING this Equation?
17.
Sally bought three candy bars for a total of $18.00. How much did each candy bar cost? Write an equation to solve this problem. Use c as your variable.
a)
18c=6
b)
c + 6= 18
c)
c +18 = 6
d)
3c=18
18.
Oranges cost $2 per pound. How many pounds of oranges can you buy for $20?
a)
a/2 = 20
b)
2a = 20
c)
20/a = 2
d)
2/a = 20
19.
331 students went on a field trip. Six buses were filled and 7 students traveled in cars. How many students were in each bus? Write an equation that matches this situation.
a)
331=7x+6
b)
331=13x
c)
331=6x+7
d)
331-7=6x
20.
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
WaygroundAnswer Key

Solving One and Two Step Linear Equations

Total questions: 20

1.
b)

Find the value of the variable that makes the statement true

, e)

Get the Variable BY ITSELF!

2.
a)

What you do on one side you must do to the other (keep balanced)

, c)

Always use the opposite/inverse operations to solve

3.
c)

Divide both sides by -8

4.
a)

g = 3

5.
b)

add 10 to both sides

6.
c)

Multiply by 5 on both sides

7.
a)

Add 6 to both sides and then divide both sides by 5

8.
c)

k = -4

9.
c)

h = -7

10.
d)

n = 48

11.
c)

p = 4

12.
b)

h = 20

13.
c)

e = -8

14.
c) a= -5
15.
a)

h = 9.4

16.
a)
17.
d) 3c=18
18.
b) 2a = 20
19.
c) 331=6x+7
20.
a) 7x + 35 = 63

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FAQs

What does the Solving One and Two Step Linear Equations worksheet cover?

This worksheet uses 2 multiple-select and 18 multiple-choice questions to practice isolating a variable and keeping equations balanced through inverse operations. Students identify the correct operation and solving sequence, then solve equations with integer, fractional, decimal, positive, and negative values, such as 3p + 7 = 19 and 3.2e + 2.6 = -23.

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

Begin by using the first two multiple-select questions to discuss the goal of finding the variable value and the rule that an operation applied to one side must also be applied to the other. Then model the step-selection items, including adding 10 before dividing by 5 and multiplying by 5 after subtracting 7, before assigning the equation-solving questions for guided or independent practice.

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

Watch for students choosing an operation that does not undo the term attached to the variable, applying an operation to only one side, or reversing the order of steps in two-step equations. The multiple-choice distractors also reveal sign and arithmetic errors, such as selecting h = 7 instead of h = -7 in 6h = -42 or failing to divide by a negative coefficient.

How do I assign and grade this linear 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 20 questions. Printable submissions can be graded by scanning student work with the Wayground for Teachers app. The printable PDF also gives schools an option for reducing screen time during equation practice.

How can I differentiate this linear equations worksheet for my students?

Use the worksheet’s Advanced Settings to adjust font spacing or choose a larger font size so the equations, answer choices, and multi-step prompts are easier to read. You can also enable a dyslexia-friendly font or translate the worksheet into another language while preserving its multiple-select and multiple-choice format.

Where can I find more free worksheets like this on Wayground?

Wayground offers a comprehensive 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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