Free Grade 3 Introducing Two-step Equations Word Problems Worksheets
Free Grade 3 worksheets for Introducing Two-step Equations Word Problems: 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
20 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify introducing two-step equations word problems
Identify introducing two-step equations word problems accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain introducing two-step equations word problems
Explain introducing two-step equations word problems accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing two-step equations word problems
Calculate introducing two-step equations word problems accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing two-step equations word problems
Compare introducing two-step equations word problems 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 Introducing Two-step Equations Word Problems 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 + 6 = 17.[1]
- 2.Solve x + 12 = 12.[1]
- 3.Solve x + 17 = 25.[1]
- 4.Solve x + 7 = 7.[1]
- 5.Solve 6x + 20 = 74.[2]
- 6.Solve 5x + 2 = 62.[2]
- 7.Solve 7x + 13 = 13.[2]
- 8.Solve 3x + 15 = 45.[2]
- 9.Solve 9x + 4 = 4x + 39.[3]
- 10.Solve 9x + 19 = 6x + -8.[3]
- 11.Solve 4x + 9 = 2x + 15.[3]
- 12.Solve 5x + 2 = 2x + -1.[3]
Show answers and working
1. x = 11
Subtract 6 from both sides: x = 11. Check: 1 × 11 + 6 = 17.
2. x = 0
Subtract 12 from both sides: x = 0. Check: 1 × 0 + 12 = 12.
3. x = 8
Subtract 17 from both sides: x = 8. Check: 1 × 8 + 17 = 25.
4. x = 0
Subtract 7 from both sides: x = 0. Check: 1 × 0 + 7 = 7.
5. x = 9
Subtract 20 from both sides: 6x = 54. Divide by 6: x = 9. Check: 6 × 9 + 20 = 74.
6. x = 12
Subtract 2 from both sides: 5x = 60. Divide by 5: x = 12. Check: 5 × 12 + 2 = 62.
7. x = 0
Subtract 13 from both sides: 7x = 0. Divide by 7: x = 0. Check: 7 × 0 + 13 = 13.
8. x = 10
Subtract 15 from both sides: 3x = 30. Divide by 3: x = 10. Check: 3 × 10 + 15 = 45.
9. x = 7
Subtract 4x from both sides: 5x + 4 = 39. Subtract 4: 5x = 35. Divide by 5: x = 7.
10. x = -9
Subtract 6x from both sides: 3x + 19 = -8. Subtract 19: 3x = -27. Divide by 3: x = -9.
11. x = 3
Subtract 2x from both sides: 2x + 9 = 15. Subtract 9: 2x = 6. Divide by 2: x = 3.
12. x = -1
Subtract 2x from both sides: 3x + 2 = -1. Subtract 2: 3x = -3. Divide by 3: x = -1.
Worked examples
Solve x + 7 = 11.
- Subtract 7 from both sides: x = 4.
- Check: 1 × 4 + 7 = 11.
- Answer: x = 4
Solve 2x + 14 = 14.
- Subtract 14 from both sides: 2x = 0.
- Divide by 2: x = 0.
- Check: 2 × 0 + 14 = 14.
- Answer: x = 0
Solve 9x + 8 = 4x + 43.
- Subtract 4x from both sides: 5x + 8 = 43.
- Subtract 8: 5x = 35.
- Divide by 5: x = 7.
- Answer: x = 7
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.
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Frequently asked
- Is this Grade 3 Introducing Two-step Equations Word Problems 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 Introducing Two-step Equations Techniques, Introducing Two-step Equations Essentials, One-step Equations. 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 Introducing Two-step Equations Word Problems?
- Move on to Introducing Two-step Equations Common Errors, Working with Two-step Equations, Two-step Equations in Context, which build directly on this idea.
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