Free Grade 3 Working with Working with Two-step Equations Techniques Worksheets
Free Grade 3 worksheets for Working with Working with Two-step Equations Techniques: 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
Higher
15 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify working with working with two-step equations techniques
Identify working with working with two-step equations techniques accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain working with working with two-step equations techniques
Explain working with working with two-step equations techniques accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with working with two-step equations techniques
Calculate working with working with two-step equations techniques accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with working with two-step equations techniques
Compare working with working with two-step equations techniques 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 Working with Working with Two-step Equations Techniques 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 + 16 = 24.[1]
- 2.Solve x + 4 = 14.[1]
- 3.Solve x + 10 = 16.[1]
- 4.Solve x + 17 = 29.[1]
- 5.Solve 8x + 8 = 48.[2]
- 6.Solve 5x + 19 = 24.[2]
- 7.Solve 7x + 11 = 4.[2]
- 8.Solve 2x + 8 = 16.[2]
- 9.Solve 4x + 6 = 2x + -6.[3]
- 10.Solve 9x + 1 = 1x + -47.[3]
- 11.Solve 9x + 12 = 3x + 6.[3]
- 12.Solve 8x + 16 = 7x + 11.[3]
Show answers and working
1. x = 8
Subtract 16 from both sides: x = 8. Check: 1 × 8 + 16 = 24.
2. x = 10
Subtract 4 from both sides: x = 10. Check: 1 × 10 + 4 = 14.
3. x = 6
Subtract 10 from both sides: x = 6. Check: 1 × 6 + 10 = 16.
4. x = 12
Subtract 17 from both sides: x = 12. Check: 1 × 12 + 17 = 29.
5. x = 5
Subtract 8 from both sides: 8x = 40. Divide by 8: x = 5. Check: 8 × 5 + 8 = 48.
6. x = 1
Subtract 19 from both sides: 5x = 5. Divide by 5: x = 1. Check: 5 × 1 + 19 = 24.
7. x = -1
Subtract 11 from both sides: 7x = -7. Divide by 7: x = -1. Check: 7 × -1 + 11 = 4.
8. x = 4
Subtract 8 from both sides: 2x = 8. Divide by 2: x = 4. Check: 2 × 4 + 8 = 16.
9. x = -6
Subtract 2x from both sides: 2x + 6 = -6. Subtract 6: 2x = -12. Divide by 2: x = -6.
10. x = -6
Subtract 1x from both sides: 8x + 1 = -47. Subtract 1: 8x = -48. Divide by 8: x = -6.
11. x = -1
Subtract 3x from both sides: 6x + 12 = 6. Subtract 12: 6x = -6. Divide by 6: x = -1.
12. x = -5
Subtract 7x from both sides: 1x + 16 = 11. Subtract 16: 1x = -5. Divide by 1: x = -5.
Worked examples
Solve x + 18 = 22.
- Subtract 18 from both sides: x = 4.
- Check: 1 × 4 + 18 = 22.
- Answer: x = 4
Solve 6x + 16 = 4.
- Subtract 16 from both sides: 6x = -12.
- Divide by 6: x = -2.
- Check: 6 × -2 + 16 = 4.
- Answer: x = -2
Solve 6x + 18 = 2x + 42.
- Subtract 2x from both sides: 4x + 18 = 42.
- Subtract 18: 4x = 24.
- Divide by 4: 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.
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Frequently asked
- Is this Grade 3 Working with Working with Two-step Equations Techniques 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 Rules and Methods in Working with Two-step Equations Techniques, Key Vocabulary of Working with Two-step Equations Techniques, Working with Two-step Equations Essentials. 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 Working with Working with Two-step Equations Techniques?
- Move on to Working with Two-step Equations Techniques in Examinations, Working with Two-step Equations Essentials, Working with Two-step Equations Word Problems, Working with Two-step Equations Common Errors, which build directly on this idea.
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