MathsFreePrintable

Two-Step Linear Equations

A free maths worksheet ready for your classroom. Open in Kuraplan to grab the print-ready PDF, customize it for your students, or generate a fresh version in seconds.

Two-Step Linear Equations worksheet preview
Two-Step Linear Equations

Two-Step Linear Equations

Algebraic equations illustration

🔢 Part 1: Solving Two-Step Equations

Instructions: Solve each equation step by step. Show all your working and check your answers by substituting back into the original equation.

1. 4x + 5 = 17
2. 7y - 2 = 26
3. 3a + 9 = 21
4. 6b - 4 = 32
5. 2m + 7 = 19

📝 Part 2: Word Problems to Equations

Instructions: Read each problem carefully. Write an equation to represent the situation, then solve it.

6. Lucy has some marbles. She buys 8 more and now has 20 marbles in total. How many marbles did she have before?

Let x = number of marbles Lucy had before

Equation: _________________

7. James saves some money each week. After saving for 5 weeks and adding an extra $12 from his birthday, he has $47. How much does he save each week?

Let w = amount James saves each week

Equation: _________________

8. A taxi ride costs $3.50 plus $2.20 per kilometre. If Sarah's taxi ride cost $14.30, how many kilometres did she travel?

Let k = number of kilometres travelled

Equation: _________________

✅ Part 3: Multiple Choice

Instructions: Circle the correct answer for each question.

9. What is the first step to solve 3x + 8 = 20?

Divide both sides by 3

Subtract 8 from both sides

Add 8 to both sides

Multiply both sides by 3

10. If 2y - 5 = 11, what is the value of y?

y = 3

y = 8

y = 13

y = 16

11. Which equation represents: "A number multiplied by 4, then decreased by 7, equals 21"?

4x + 7 = 21

4x - 7 = 21

7x - 4 = 21

x/4 - 7 = 21

🔍 Part 4: Check Your Understanding

12. Fill in the blanks to complete the solution:

To solve 5x + 3 = 23:

Step 1: ________ 3 from both sides to get 5x = ________

Step 2: ________ both sides by 5 to get x = ________

Check: 5(____) + 3 = ________ ✓

13. Explain in your own words why we use inverse operations to solve equations:
14. Create your own word problem that can be solved using a two-step equation:
15. Write the equation for your word problem and solve it:

🎯 Part 5: Challenge Problems

16. Solve: 8 - 3x = 2
17. The perimeter of a rectangle is 24 metres. If the width is 4 metres, what is the length?

Remember: Perimeter = 2 × length + 2 × width

Equation: _________________

About This Worksheet

Free in Kuraplan

Sign up free, grab the PDF, and customize it for your class.

Print-Ready

Formatted for standard paper. Clean layout, easy to read.

AI-Generated

Created with Kuraplan's AI, designed for real classroom use.

For Teachers & Parents

Use in classrooms, for homework, tutoring, or homeschool.

Need a custom version of this worksheet?

Kuraplan's AI generates custom worksheets in seconds — differentiated for every learner, aligned to your curriculum.

Generate Custom Worksheets — Free
No credit card Curriculum-aligned Under 60 seconds