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MC 2.4 - Solving Equations with variables on both sides Alg 1 V1 - Printable Mathematics Worksheets - Wayground

MC 2.4 - Solving Equations with variables on both sides Alg 1 V1

10 questions

9th - 9th Grade

Mathematics

MC 2.4 - Solving Equations with Variables on Both Sides gives Grade 9 students focused Algebra 1 practice solving linear equations in which variable terms and constants may appear on both sides of the equal sign. The worksheet combines multiple-choice and multiple-select items covering isolation of the variable, applying inverse operations, maintaining equality on both sides, distributing before solving, and identifying equations with infinite solutions. Students solve equations such as 4k + 24 = 6k - 10 and 12 - 5k = k + 6, then demonstrate conceptual understanding by selecting valid solving rules and identifying the objective of equation solving. The practice also asks students to recognize when simplifying both sides produces infinitely many solutions. This free printable worksheet includes a complete answer key and can support independent practice, guided instruction, review, or a quick check of Grade 9 students’ equation-solving understanding.

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MC 2.4 - Solving Equations with variables on both sides Alg 1 V1

Total questions: 10

Name
Class
Date
1.

4k + 24 = 6k -10

a)

k = 17

b)

k =-17

c)

k= 5

d)

k = 1/5

2.

3y + 16 = 5y

a)

y = 8

b)

y = -8

c)

y = 1/8

d)

y = -1/8

3.

13y - 18 = -5y + 36

a)

y = 3

b)

y = -3

c)

y= 9

d)

y = -9

4.

13x = 32 + 5x

a)

x = 4

b)

x = -4

c)

x = 1/4

d)

x = -1/4

5.

12 - 5k = k + 6

a)

k = 1

b)

k -1

c)

k= 1/2

d)

k = -1/2

6.
The objective when solving an equation is to....
a)
isolate the variable.
b)
check the solution.
c)
guess and check.
d)
Combine Like Terms.
7.

Which of the following are basic rules used for solving algebraic equations?

a)

Whatever you do to one side of the equal sign, you must copy and do on the other side of the equal sign

b)

Negative signs can be ignored

c)

Always start on the left side, regardless of where the variable is

d)

Always do the opposite operation

8.

What is the first step in solving this equation?

a)

add 4 to both sides

b)

distribute the 4

c)

subtract 4 to both sides

d)

subtract 12 to both sides

9.

1 + 3p + 6 = 3p + 151\ +\ 3p\ +\ 6\ =\ 3p\ +\ 15  

a)

-2

b)

-16

c)

All Real Numbers

d)

No Solution

10.

3(x-8)=3x-24

a)

No Solution

b)

x=3

c)

Infinite Solutions

d)

x=-3

Answer Key

MC 2.4 - Solving Equations with variables on both sides Alg 1 V1

Total questions: 10

1.
a)

k = 17

2.
a)

y = 8

3.
a)

y = 3

4.
a)

x = 4

5.
a)

k = 1

6.
a) isolate the variable.
7.
a)

Whatever you do to one side of the equal sign, you must copy and do on the other side of the equal sign

, d)

Always do the opposite operation

8.
b)

distribute the 4

9.
d)

No Solution

10.
c)

Infinite Solutions

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FAQs

What does this worksheet cover?

This Grade 9 Algebra 1 worksheet focuses on solving linear equations with variables on both sides, using multiple-choice and multiple-select questions. Students practice isolating the variable, applying opposite operations to both sides, distributing before solving, and recognizing when an equation has infinite solutions.

How can I use this worksheet to teach solving equations with variables on both sides?

Use the computational items to model a consistent sequence: simplify by distributing when needed, collect variable terms and constants, apply inverse operations, and isolate the variable. Before students work independently, use the rule-selection question to discuss why the same operation must be performed on both sides and why opposite operations help undo terms. Finish by having students explain why 3(x - 8) = 3x - 24 has infinite solutions rather than one numerical solution.

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

Watch for students moving a term across the equal sign without applying the corresponding inverse operation, ignoring negative signs, or performing an operation on only one side. Students may also choose a first step such as subtracting a constant when distribution is required, or report a single value for an identity such as 3(x - 8) = 3x - 24 instead of recognizing infinite solutions.

How do I assign and grade this worksheet?

On Wayground, assign it as a printable PDF or as a digital quiz, and use the complete answer key to check the multiple-choice and multiple-select responses. Printable submissions can be graded by scanning student work with the Wayground for Teachers app. The printable format also supports schools that are reducing screen time.

How can I differentiate this worksheet for my students?

In the worksheet’s Advanced Settings, adjust font size or spacing to make the linear equations and answer choices easier to read. You can also apply a dyslexia-friendly font or translate the worksheet into another language, depending on students’ reading and language needs.

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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