Free Grade 3 Working with Equations with Unknowns Both Sides Flashcards
Free Grade 3 flashcards for Working with Equations with Unknowns Both Sides: 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.
- UnderstandExplain working with equations with unknowns both sides
Explain working with equations with unknowns both sides accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with equations with unknowns both sides
Calculate working with equations with unknowns both sides accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with equations with unknowns both sides
Compare working with equations with unknowns both sides accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify working with equations with unknowns both sides
Justify working with equations with unknowns both sides 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 Equations with Unknowns Both Sides 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 + 19 = 27.[1]
- 2.Solve x + 8 = 11.[1]
- 3.Solve x + 12 = 12.[1]
- 4.Solve x + 20 = 28.[1]
- 5.Solve 3x + 13 = 1.[2]
- 6.Solve 9x + 15 = -12.[2]
- 7.Solve 9x + 15 = 96.[2]
- 8.Solve 7x + 13 = 41.[2]
- 9.Solve 9x + 4 = 4x + -11.[3]
- 10.Solve 7x + 1 = 5x + 15.[3]
- 11.Solve 8x + 19 = 6x + 21.[3]
- 12.Solve 3x + 16 = 1x + 6.[3]
Show answers and working
1. x = 8
Subtract 19 from both sides: x = 8. Check: 1 × 8 + 19 = 27.
2. x = 3
Subtract 8 from both sides: x = 3. Check: 1 × 3 + 8 = 11.
3. x = 0
Subtract 12 from both sides: x = 0. Check: 1 × 0 + 12 = 12.
4. x = 8
Subtract 20 from both sides: x = 8. Check: 1 × 8 + 20 = 28.
5. x = -4
Subtract 13 from both sides: 3x = -12. Divide by 3: x = -4. Check: 3 × -4 + 13 = 1.
6. x = -3
Subtract 15 from both sides: 9x = -27. Divide by 9: x = -3. Check: 9 × -3 + 15 = -12.
7. x = 9
Subtract 15 from both sides: 9x = 81. Divide by 9: x = 9. Check: 9 × 9 + 15 = 96.
8. x = 4
Subtract 13 from both sides: 7x = 28. Divide by 7: x = 4. Check: 7 × 4 + 13 = 41.
9. x = -3
Subtract 4x from both sides: 5x + 4 = -11. Subtract 4: 5x = -15. Divide by 5: x = -3.
10. x = 7
Subtract 5x from both sides: 2x + 1 = 15. Subtract 1: 2x = 14. Divide by 2: x = 7.
11. x = 1
Subtract 6x from both sides: 2x + 19 = 21. Subtract 19: 2x = 2. Divide by 2: x = 1.
12. x = -5
Subtract 1x from both sides: 2x + 16 = 6. Subtract 16: 2x = -10. Divide by 2: x = -5.
Worked examples
Solve x + 3 = 15.
- Subtract 3 from both sides: x = 12.
- Check: 1 × 12 + 3 = 15.
- Answer: x = 12
Solve 2x + 12 = 24.
- Subtract 12 from both sides: 2x = 12.
- Divide by 2: x = 6.
- Check: 2 × 6 + 12 = 24.
- Answer: x = 6
Solve 8x + 3 = 4x + -25.
- Subtract 4x from both sides: 4x + 3 = -25.
- Subtract 3: 4x = -28.
- Divide by 4: 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 Working with Equations with Unknowns Both Sides flashcards really free?
- Yes. Every flashcards 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 Unknowns Both Sides, Equations with Brackets. Each one has its own free lesson, worksheet and quiz.
- How is the flashcards 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 Equations with Unknowns Both Sides?
- Move on to Equations with Unknowns Both Sides in Context, One-step Equations, Two-step Equations, Equations with Brackets, which build directly on this idea.
Related resources
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