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Steps to Solving Equations with Variables on Both Sides - Printable Mathematics Worksheets class 8 - Wayground

Steps to Solving Equations with Variables on Both Sides

23 questions

8th - 8th Grade

Mathematics

Steps to Solving Equations with Variables on Both Sides is a free Grade 8 mathematics worksheet that helps students choose and apply the correct sequence for solving multi-step equations. Students identify the goal of solving an equation, determine the best first or next step, recognize when to use the distributive property, combine like terms, move variable terms to one side, and apply inverse operations to isolate the variable. Several questions ask students to select every step that applies, while others analyze a worked solution and identify the operation used between steps.

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Worksheets

Steps to Solving Equations with Variables on Both Sides

Total questions: 23

Name
Class
Date
1.

The goal of solving a one, two, or multi-step equations is to:

a)

Find the constant

b)

Find the coefficient

c)

Find the value of the variable

d)

Get rid of the variable

2.

What is the first step you should take to solve this equation:

 −11−3x=44−2x-11-3x=44-2x  

a)

Add 3 to both sides

b)

Isolate the variable on one side

c)

Subtract 11 from both sides

d)

Divide both sides by -3

3.

What is the first step you should take to solve this equation:

 3(x−2)=2x+73\left(x-2\right)=2x+7  

a)

Add 2 to both sides

b)

Use distributive property to get rid of the parentheses

c)

Isolate the variable on one side

d)

Subtract 7 from both sides

4.

Check all steps that you would need to take to solve this equation:

 8(2x−3)+2x=4x−48\left(2x-3\right)+2x=4x-4  

a)

Use distributive property to get rid of parentheses

b)

Combine like terms

c)

Move the variable to one side of the equation

d)

Use inverse operations to isolate and solve for the variable.

5.

Check all steps that you would need to take to solve this equation:


 4x−2=−2x+164x-2=-2x+16  

a)

Use distributive property to get rid of parentheses

b)

Combine like terms

c)

Move the variable to one side of the equation

d)

Use inverse operations to isolate and solve for the variable.

6.

Check all steps that you would need to take to solve this equation:

 4x+7−2x=18−3x4x+7-2x=18-3x  

a)

Use distributive property to get rid of parentheses

b)

Combine like terms

c)

Move the variable to one side of the equation

d)

Use inverse operations to isolate and solve for the variable.

7.

Check all steps that you would need to take to solve this equation:

 4(x−2)=x+14\left(x-2\right)=x+1  

a)

Use distributive property to get rid of parentheses

b)

Combine like terms

c)

Move the variable to one side of the equation

d)

Use inverse operations to isolate and solve for the variable

8.

Check all that apply - What could you do to move the variable to one side of this equation:
 2x+3=4x−72x+3=4x-7 

a)

Subtract 2x from both sides

b)

Subtract 3 from both sides

c)

Subtract 4x from both sides

d)

Add 7 to both sides

9.

Jacob solved the following equation using the steps shown.

Step 1 5x + 9 = 2x - 3

Step 2 3x + 9 = -3

Step 3 3x = -12

Step 4 x = -4

What operation did he perform to get from Step 1 to Step 2?

a)

Subtracted 2x from both sides of the equation

b)

Subtracted 9 from both sides of the equation

c)

Multiplied both sides of the equation by 3

d)

Added -3 to both sides of the equation

10.

What would be the best first step to solve the equation:

1+18n=361+18n=36  

a)

Add 1 to both sides

b)

Collect the numbers to the right

c)

Divide 36 by 18

d)

Subtract 1 from both sides

11.

What would be the best first step to solve this equation:

11−3x=4411-3x=44  

a)

Add 3 to both sides

b)

Add 11 to both sides

c)

Subtract 11 from both sides

d)

Divide by 3 on both sides

12.

What would be the best next step in solving this equation:

1+4n=10−14n1+4n=10-14n  

a)

Subtract 14n from both sides

b)

Add 14n to both sides

c)

Add 10 to both sides

13.

Which of the following steps for the equation below results in a positive coefficient for x?

4x−3=2x+154x-3=2x+15  

a)

Subtract 4x from both sides

b)

Add 3 to both sides

c)

Subtract 15 from both sides

d)

Subtract 2x from both sides

14.

Jasmine solve the following equation using the steps shown:
Step 1:  6x+9=3x−36x+9=3x-3  

Step 2:  3x+9=−33x+9=-3  

Step 3:  3x=−123x=-12  

Step 4:  x=−4x=-4  


What operation did she perform to get from Step 1 to Step 2? 

a)

Subtract 3x from both sides

b)

Divide both sides by 3

c)

Subtract 9 from both sides

d)

Divide both sides by 2

15.

Solve:

2x−5=3x+42x-5=3x+4  

 

Enter only the value of x, not "x = (a)   ".  No spaces.

16.

Solve:

5w+5=8w−105w+5=8w-10  

a)

-5

b)

2

c)

-2

d)

5

17.

Solve:

8x−8=−4x+168x-8=-4x+16  

a)

8

b)

2

c)

16

d)

24

18.

Solve:

7x=5x−167x=5x-16  

 

Enter only the value of x, not "x = (a)   ".  No spaces.

19.

Solve:

−3+2a=9−4a-3+2a=9-4a  

 

Enter only the value of x, not "a = (a)   ".  No spaces.

20.

6a+3−4a=96a+3-4a=9

Solve:

a)

a = 3

b)

a = 9

c)

a = 6

d)

a = -3

21.

3x+8−x=5x−43x+8-x=5x-4  

Is 4 a solution to the equation:

a)

yes

b)

maybe

c)

no

22.

Solve:

10h+12=8h+410h+12=8h+4  

 

Enter only the value of x, not "h = (a)   ".  No spaces.

23.

Solve:

5p+8=7p+25p+8=7p+2  

 

Enter only the value of x, not "p = (a)   ".  No spaces.

Answer Key

Steps to Solving Equations with Variables on Both Sides

Total questions: 23

1.
c)

Find the value of the variable

2.
b)

Isolate the variable on one side

3.
b)

Use distributive property to get rid of the parentheses

4.
d)

Use inverse operations to isolate and solve for the variable.

, c)

Move the variable to one side of the equation

, b)

Combine like terms

, a)

Use distributive property to get rid of parentheses

5.
d)

Use inverse operations to isolate and solve for the variable.

, c)

Move the variable to one side of the equation

6.
d)

Use inverse operations to isolate and solve for the variable.

, c)

Move the variable to one side of the equation

, b)

Combine like terms

7.
d)

Use inverse operations to isolate and solve for the variable

, c)

Move the variable to one side of the equation

, a)

Use distributive property to get rid of parentheses

8.
a)

Subtract 2x from both sides

, c)

Subtract 4x from both sides

9.
a)

Subtracted 2x from both sides of the equation

10.
d)

Subtract 1 from both sides

11.
c)

Subtract 11 from both sides

12.
b)

Add 14n to both sides

13.
d)

Subtract 2x from both sides

14.
a)

Subtract 3x from both sides

15.
-9
16.
d)

5

17.
b)

2

18.
-8
19.
2
20.
a)

a = 3

21.
a)

yes

22.
-4
23.
3

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FAQs

What does this worksheet cover?

This Grade 8 worksheet focuses on selecting and sequencing the steps used to solve equations with variables on both sides. Its 23 items include multiple-choice questions, multiple-select questions, and fill-in-the-blank problems covering distribution, combining like terms, moving variable terms, applying inverse operations, analyzing worked steps, and solving for the variable.

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

Use the worksheet after modeling a consistent process: simplify each side, move variable terms to one side, use inverse operations to isolate the variable, and check the result. Before students work independently, have them explain why a particular equation requires distribution or combining like terms, and use the multiple-select items to discuss why some possible operations are unnecessary.

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

Watch for students choosing an operation that changes constants instead of moving variable terms, skipping distribution before combining terms, or selecting every listed step in a multiple-select item rather than only the steps required. In the worked-solution questions, students may also misidentify the operation between two lines or reverse the sign when moving a term across the equal sign.

How do I assign and grade this worksheet?

This worksheet is available as a printable PDF and as a digital quiz on Wayground, and it includes a complete answer key. You can grade printable submissions by scanning student work with the Wayground for Teachers app, or review responses from the digital quiz. The printable format also supports schools that want to reduce screen time.

How can I differentiate this worksheet for my students?

Because the worksheet combines algebraic notation with multi-step and multiple-select questions, you can adjust font size and spacing to make equations and answer choices easier to read. In the worksheet’s Advanced Settings, you can also select a dyslexia-friendly font or translate the worksheet into another language when appropriate.

Where can I find more worksheets like this on Wayground?

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