Free Grade 3 Working with Two-step Equations Quizzes
Free Grade 3 quizzes for Working with 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.
- UnderstandExplain working with two-step equations
Explain working with two-step equations accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with two-step equations
Calculate working with two-step equations accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with two-step equations
Compare working with two-step equations accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify working with two-step equations
Justify working with 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 Working with 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 + 8 = 10.[1]
- 2.Solve x + 5 = 15.[1]
- 3.Solve x + 5 = 7.[1]
- 4.Solve x + 7 = 14.[1]
- 5.Solve 8x + 9 = -31.[2]
- 6.Solve 6x + 11 = 29.[2]
- 7.Solve 6x + 2 = 68.[2]
- 8.Solve 7x + 18 = 95.[2]
- 9.Solve 7x + 9 = 6x + 2.[3]
- 10.Solve 6x + 12 = 5x + 10.[3]
- 11.Solve 4x + 20 = 3x + 15.[3]
- 12.Solve 8x + 7 = 7x + 18.[3]
Show answers and working
1. x = 2
Subtract 8 from both sides: x = 2. Check: 1 × 2 + 8 = 10.
2. x = 10
Subtract 5 from both sides: x = 10. Check: 1 × 10 + 5 = 15.
3. x = 2
Subtract 5 from both sides: x = 2. Check: 1 × 2 + 5 = 7.
4. x = 7
Subtract 7 from both sides: x = 7. Check: 1 × 7 + 7 = 14.
5. x = -5
Subtract 9 from both sides: 8x = -40. Divide by 8: x = -5. Check: 8 × -5 + 9 = -31.
6. x = 3
Subtract 11 from both sides: 6x = 18. Divide by 6: x = 3. Check: 6 × 3 + 11 = 29.
7. x = 11
Subtract 2 from both sides: 6x = 66. Divide by 6: x = 11. Check: 6 × 11 + 2 = 68.
8. x = 11
Subtract 18 from both sides: 7x = 77. Divide by 7: x = 11. Check: 7 × 11 + 18 = 95.
9. x = -7
Subtract 6x from both sides: 1x + 9 = 2. Subtract 9: 1x = -7. Divide by 1: x = -7.
10. x = -2
Subtract 5x from both sides: 1x + 12 = 10. Subtract 12: 1x = -2. Divide by 1: x = -2.
11. x = -5
Subtract 3x from both sides: 1x + 20 = 15. Subtract 20: 1x = -5. Divide by 1: x = -5.
12. x = 11
Subtract 7x from both sides: 1x + 7 = 18. Subtract 7: 1x = 11. Divide by 1: x = 11.
Worked examples
Solve x + 4 = 14.
- Subtract 4 from both sides: x = 10.
- Check: 1 × 10 + 4 = 14.
- Answer: x = 10
Solve 7x + 3 = 38.
- Subtract 3 from both sides: 7x = 35.
- Divide by 7: x = 5.
- Check: 7 × 5 + 3 = 38.
- Answer: x = 5
Solve 6x + 11 = 1x + 66.
- Subtract 1x from both sides: 5x + 11 = 66.
- Subtract 11: 5x = 55.
- Divide by 5: x = 11.
- Answer: x = 11
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 Working with Two-step Equations
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Frequently asked
- Is this Grade 3 Working with Two-step Equations quiz really free?
- Yes. Every quizzes 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, One-step Equations. Each one has its own free lesson, worksheet and quiz.
- How is the quiz 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 Two-step Equations?
- Move on to Two-step Equations in Context, One-step Equations, Equations with Brackets, Equations with Unknowns Both Sides, which build directly on this idea.
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