Free Grade 3 Working with Inequality Notation Flashcards
Free Grade 3 flashcards for Working with Inequality Notation: 12 real questions with a full answer key and worked solutions. An inequality gives a range of values. Solve it like an equation, but if you multiply or divide by a negative, flip the sign.
Free
Higher
15 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain working with inequality notation
Explain working with inequality notation accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with inequality notation
Calculate working with inequality notation accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with inequality notation
Compare working with inequality notation accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify working with inequality notation
Justify working with inequality notation 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 Inequality Notation works
An inequality gives a range of values. Solve it like an equation, but if you multiply or divide by a negative, flip the sign.
12 practice questions
Easy to hard, 24 marks in total. Try them first, then open the answers.
- 1.Solve 4x + 4 ≥ 16.[1]
- 2.Solve 3x + 8 > 20.[1]
- 3.Solve 6x + 9 < 21.[1]
- 4.Solve 4x + 2 > 14.[1]
- 5.Solve 6x + 2 ≥ 20.[2]
- 6.Solve 2x + 4 ≤ 22.[2]
- 7.Solve 5x + 8 > 23.[2]
- 8.Solve 2x + 14 < 28.[2]
- 9.Solve 5x + 1 ≥ 11 and list the positive integers that satisfy it (if finite).[3]
- 10.Solve 5x + 4 ≥ 19 and list the positive integers that satisfy it (if finite).[3]
- 11.Solve 6x + 15 ≤ 51 and list the positive integers that satisfy it (if finite).[3]
- 12.Solve 4x + 12 > 40 and list the positive integers that satisfy it (if finite).[3]
Show answers and working
1. x ≥ 3
Subtract 4: 4x ≥ 12. Divide by 4 (positive, so the sign stays): x ≥ 3.
2. x > 4
Subtract 8: 3x > 12. Divide by 3 (positive, so the sign stays): x > 4.
3. x < 2
Subtract 9: 6x < 12. Divide by 6 (positive, so the sign stays): x < 2.
4. x > 3
Subtract 2: 4x > 12. Divide by 4 (positive, so the sign stays): x > 3.
5. x ≥ 3
Subtract 2: 6x ≥ 18. Divide by 6 (positive, so the sign stays): x ≥ 3.
6. x ≤ 9
Subtract 4: 2x ≤ 18. Divide by 2 (positive, so the sign stays): x ≤ 9.
7. x > 3
Subtract 8: 5x > 15. Divide by 5 (positive, so the sign stays): x > 3.
8. x < 7
Subtract 14: 2x < 14. Divide by 2 (positive, so the sign stays): x < 7.
9. x ≥ 2
Subtract 1: 5x ≥ 10. Divide by 5 (positive, so the sign stays): x ≥ 2.
10. x ≥ 3
Subtract 4: 5x ≥ 15. Divide by 5 (positive, so the sign stays): x ≥ 3.
11. x ≤ 6
Subtract 15: 6x ≤ 36. Divide by 6 (positive, so the sign stays): x ≤ 6.
12. x > 7
Subtract 12: 4x > 28. Divide by 4 (positive, so the sign stays): x > 7.
Worked examples
Solve 3x + 13 > 40.
- Subtract 13: 3x > 27.
- Divide by 3 (positive, so the sign stays): x > 9.
- Answer: x > 9
Solve 4x + 13 > 29.
- Subtract 13: 4x > 16.
- Divide by 4 (positive, so the sign stays): x > 4.
- Answer: x > 4
Solve 5x + 11 ≥ 31 and list the positive integers that satisfy it (if finite).
- Subtract 11: 5x ≥ 20.
- Divide by 5 (positive, so the sign stays): x ≥ 4.
- Answer: x ≥ 4
Interactive practice
Free, no account required — answer on screen or print it.
Common mistakes
What learners typically get wrong, and how to fix it.
Forgets to flip the sign when dividing by a negative.
Correction: Test a value to check the direction.
Mixes up < and ≤.
Correction: ≤ includes the boundary; show it with a filled circle.
Teacher tips
- · Show every answer on a number line.
Parent tips
- · Talk about 'at least' and 'no more than' on signs.
Real-life applications
- · Age limits, speed limits, minimum orders.
Assessment objectives
How mastery is evidenced, and which standards it maps to.
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Frequently asked
- Is this Grade 3 Working with Inequality Notation 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 Inequality Notation, Equations. 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 Inequality Notation?
- Move on to Inequality Notation in Context, Solving Linear Inequalities, Inequalities on a Number Line, which build directly on this idea.
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