Free Grade 3 Equations with Brackets Worksheets
Free Grade 3 worksheets for Equations with Brackets: 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
Stretch
20 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain equations with brackets
Explain equations with brackets accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate equations with brackets
Calculate equations with brackets accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare equations with brackets
Compare equations with brackets accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify equations with brackets
Justify equations with brackets 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 Equations with Brackets 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 = 23.[1]
- 2.Solve x + 15 = 22.[1]
- 3.Solve x + 8 = 9.[1]
- 4.Solve x + 18 = 20.[1]
- 5.Solve 3x + 2 = -4.[2]
- 6.Solve 6x + 9 = 75.[2]
- 7.Solve 8x + 5 = -3.[2]
- 8.Solve 3x + 11 = 41.[2]
- 9.Solve 6x + 6 = 3x + -12.[3]
- 10.Solve 8x + 6 = 4x + 26.[3]
- 11.Solve 6x + 8 = 4x + 16.[3]
- 12.Solve 8x + 7 = 7x + 10.[3]
Show answers and working
1. x = 6
Subtract 17 from both sides: x = 6. Check: 1 × 6 + 17 = 23.
2. x = 7
Subtract 15 from both sides: x = 7. Check: 1 × 7 + 15 = 22.
3. x = 1
Subtract 8 from both sides: x = 1. Check: 1 × 1 + 8 = 9.
4. x = 2
Subtract 18 from both sides: x = 2. Check: 1 × 2 + 18 = 20.
5. x = -2
Subtract 2 from both sides: 3x = -6. Divide by 3: x = -2. Check: 3 × -2 + 2 = -4.
6. x = 11
Subtract 9 from both sides: 6x = 66. Divide by 6: x = 11. Check: 6 × 11 + 9 = 75.
7. x = -1
Subtract 5 from both sides: 8x = -8. Divide by 8: x = -1. Check: 8 × -1 + 5 = -3.
8. x = 10
Subtract 11 from both sides: 3x = 30. Divide by 3: x = 10. Check: 3 × 10 + 11 = 41.
9. x = -6
Subtract 3x from both sides: 3x + 6 = -12. Subtract 6: 3x = -18. Divide by 3: x = -6.
10. x = 5
Subtract 4x from both sides: 4x + 6 = 26. Subtract 6: 4x = 20. Divide by 4: x = 5.
11. x = 4
Subtract 4x from both sides: 2x + 8 = 16. Subtract 8: 2x = 8. Divide by 2: x = 4.
12. x = 3
Subtract 7x from both sides: 1x + 7 = 10. Subtract 7: 1x = 3. Divide by 1: x = 3.
Worked examples
Solve x + 9 = 12.
- Subtract 9 from both sides: x = 3.
- Check: 1 × 3 + 9 = 12.
- Answer: x = 3
Solve 4x + 16 = 60.
- Subtract 16 from both sides: 4x = 44.
- Divide by 4: x = 11.
- Check: 4 × 11 + 16 = 60.
- Answer: x = 11
Solve 5x + 3 = 2x + -12.
- Subtract 2x from both sides: 3x + 3 = -12.
- Subtract 3: 3x = -15.
- Divide by 3: 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.
Every free resource for Equations with Brackets
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Frequently asked
- Is this Grade 3 Equations with Brackets 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 Two-step Equations, 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 Equations with Brackets?
- Move on to Equations with Unknowns Both Sides, Forming Equations, Algebraic Expressions, Inequalities, which build directly on this idea.
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