Free Grade 3 Two-step Equations Worksheets
Free Grade 3 worksheets for Two-step Equations: 12 real questions with a full answer key and worked solutions. An equation is a balance. Do the same thing to both sides until the letter is on its own, then check by substituting back.
Free
Foundation
25 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify two-step equations
Identify two-step equations accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain two-step equations
Explain two-step equations accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate two-step equations
Calculate two-step equations accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare two-step equations
Compare two-step equations accurately in a familiar context.
Assessed by: Exit ticket of four short items
Prerequisites
Close these gaps first — each has its own free lesson, worksheet and quiz.
How Two-step Equations works
An equation is a balance. Do the same thing to both sides until the letter is on its own, then check by substituting back.
12 practice questions
Easy to hard, 24 marks in total. Try them first, then open the answers.
- 1.Solve x + 17 = 28.[1]
- 2.Solve x + 8 = 13.[1]
- 3.Solve x + 7 = 14.[1]
- 4.Solve x + 13 = 18.[1]
- 5.Solve 9x + 18 = 108.[2]
- 6.Solve 4x + 9 = 37.[2]
- 7.Solve 5x + 8 = 3.[2]
- 8.Solve 8x + 17 = 49.[2]
- 9.Solve 8x + 11 = 2x + -19.[3]
- 10.Solve 4x + 1 = 2x + -13.[3]
- 11.Solve 9x + 18 = 1x + 26.[3]
- 12.Solve 6x + 14 = 4x + -6.[3]
Show answers and working
1. x = 11
Subtract 17 from both sides: x = 11. Check: 1 × 11 + 17 = 28.
2. x = 5
Subtract 8 from both sides: x = 5. Check: 1 × 5 + 8 = 13.
3. x = 7
Subtract 7 from both sides: x = 7. Check: 1 × 7 + 7 = 14.
4. x = 5
Subtract 13 from both sides: x = 5. Check: 1 × 5 + 13 = 18.
5. x = 10
Subtract 18 from both sides: 9x = 90. Divide by 9: x = 10. Check: 9 × 10 + 18 = 108.
6. x = 7
Subtract 9 from both sides: 4x = 28. Divide by 4: x = 7. Check: 4 × 7 + 9 = 37.
7. x = -1
Subtract 8 from both sides: 5x = -5. Divide by 5: x = -1. Check: 5 × -1 + 8 = 3.
8. x = 4
Subtract 17 from both sides: 8x = 32. Divide by 8: x = 4. Check: 8 × 4 + 17 = 49.
9. x = -5
Subtract 2x from both sides: 6x + 11 = -19. Subtract 11: 6x = -30. Divide by 6: x = -5.
10. x = -7
Subtract 2x from both sides: 2x + 1 = -13. Subtract 1: 2x = -14. Divide by 2: x = -7.
11. x = 1
Subtract 1x from both sides: 8x + 18 = 26. Subtract 18: 8x = 8. Divide by 8: x = 1.
12. x = -10
Subtract 4x from both sides: 2x + 14 = -6. Subtract 14: 2x = -20. Divide by 2: x = -10.
Worked examples
Solve x + 17 = 20.
- Subtract 17 from both sides: x = 3.
- Check: 1 × 3 + 17 = 20.
- Answer: x = 3
Solve 3x + 12 = 27.
- Subtract 12 from both sides: 3x = 15.
- Divide by 3: x = 5.
- Check: 3 × 5 + 12 = 27.
- Answer: x = 5
Solve 4x + 13 = 3x + 19.
- Subtract 3x from both sides: 1x + 13 = 19.
- Subtract 13: 1x = 6.
- Divide by 1: x = 6.
- Answer: x = 6
Interactive practice
Free, no account required — answer on screen or print it.
Common mistakes
What learners typically get wrong, and how to fix it.
Does an operation to only one side.
Correction: Keep the balance — both sides, every time.
Uses the wrong inverse (subtracts to undo multiplying).
Correction: Undo × with ÷ and + with −.
Teacher tips
- · Always ask pupils to substitute their answer back in.
Parent tips
- · 'I think of a number' puzzles at dinner.
Real-life applications
- · Working out an unknown price or time from a total.
Assessment objectives
How mastery is evidenced, and which standards it maps to.
Every free resource for Two-step Equations
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Learn — Meet the idea.
Practice — Build fluency.
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Frequently asked
- Is this Grade 3 Two-step Equations worksheet really free?
- Yes. Every worksheets on FreeMathWorksheet is free to use, print and share — no account, no paywall and no watermark.
- What should a learner already know before this?
- Start with One-step Equations, Algebraic Expressions. Each one has its own free lesson, worksheet and quiz.
- How is the worksheet sequenced?
- Recognition first, then understanding, application, reasoning and finally mastery — the same ladder used across every free resource on the platform.
- What comes next after Two-step Equations?
- Move on to Equations with Brackets, Equations with Unknowns Both Sides, Forming Equations, Algebraic Expressions, which build directly on this idea.
Related resources
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