Free Grade 3 Introducing Equations with Brackets Techniques Worksheets
Free Grade 3 worksheets for Introducing Equations with Brackets 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.
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35 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain introducing equations with brackets techniques
Explain introducing equations with brackets techniques accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing equations with brackets techniques
Calculate introducing equations with brackets techniques accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing equations with brackets techniques
Compare introducing equations with brackets techniques accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify introducing equations with brackets techniques
Justify introducing equations with brackets 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 Introducing Equations with Brackets 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 + 11 = 12.[1]
- 2.Solve x + 7 = 18.[1]
- 3.Solve x + 3 = 12.[1]
- 4.Solve x + 6 = 8.[1]
- 5.Solve 5x + 2 = 62.[2]
- 6.Solve 9x + 17 = 26.[2]
- 7.Solve 2x + 18 = 40.[2]
- 8.Solve 8x + 2 = 90.[2]
- 9.Solve 4x + 15 = 2x + 29.[3]
- 10.Solve 6x + 12 = 5x + 22.[3]
- 11.Solve 4x + 19 = 1x + 55.[3]
- 12.Solve 8x + 14 = 7x + 11.[3]
Show answers and working
1. x = 1
Subtract 11 from both sides: x = 1. Check: 1 × 1 + 11 = 12.
2. x = 11
Subtract 7 from both sides: x = 11. Check: 1 × 11 + 7 = 18.
3. x = 9
Subtract 3 from both sides: x = 9. Check: 1 × 9 + 3 = 12.
4. x = 2
Subtract 6 from both sides: x = 2. Check: 1 × 2 + 6 = 8.
5. x = 12
Subtract 2 from both sides: 5x = 60. Divide by 5: x = 12. Check: 5 × 12 + 2 = 62.
6. x = 1
Subtract 17 from both sides: 9x = 9. Divide by 9: x = 1. Check: 9 × 1 + 17 = 26.
7. x = 11
Subtract 18 from both sides: 2x = 22. Divide by 2: x = 11. Check: 2 × 11 + 18 = 40.
8. x = 11
Subtract 2 from both sides: 8x = 88. Divide by 8: x = 11. Check: 8 × 11 + 2 = 90.
9. x = 7
Subtract 2x from both sides: 2x + 15 = 29. Subtract 15: 2x = 14. Divide by 2: x = 7.
10. x = 10
Subtract 5x from both sides: 1x + 12 = 22. Subtract 12: 1x = 10. Divide by 1: x = 10.
11. x = 12
Subtract 1x from both sides: 3x + 19 = 55. Subtract 19: 3x = 36. Divide by 3: x = 12.
12. x = -3
Subtract 7x from both sides: 1x + 14 = 11. Subtract 14: 1x = -3. Divide by 1: x = -3.
Worked examples
Solve x + 10 = 20.
- Subtract 10 from both sides: x = 10.
- Check: 1 × 10 + 10 = 20.
- Answer: x = 10
Solve 7x + 13 = 6.
- Subtract 13 from both sides: 7x = -7.
- Divide by 7: x = -1.
- Check: 7 × -1 + 13 = 6.
- Answer: x = -1
Solve 3x + 13 = 2x + 8.
- Subtract 2x from both sides: 1x + 13 = 8.
- Subtract 13: 1x = -5.
- Divide by 1: x = -5.
- Answer: x = -5
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 Equations with Brackets 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 Introducing Equations with Brackets Essentials, Two-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 Equations with Brackets Techniques?
- Move on to Introducing Equations with Brackets Word Problems, Introducing Equations with Brackets Common Errors, Working with Equations with Brackets, Equations with Brackets in Context, which build directly on this idea.
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