Free Grade 3 Inequality Notation Quizzes
Free Grade 3 quizzes for 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
30 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain inequality notation
Explain inequality notation accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate inequality notation
Calculate inequality notation accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare inequality notation
Compare inequality notation accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify inequality notation
Justify 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 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 3x + 9 ≥ 18.[1]
- 2.Solve 5x + 7 < 22.[1]
- 3.Solve 4x + 8 > 32.[1]
- 4.Solve 3x + 13 ≤ 37.[1]
- 5.Solve 5x + 8 < 28.[2]
- 6.Solve 2x + 6 > 14.[2]
- 7.Solve 6x + 14 ≥ 44.[2]
- 8.Solve 6x + 8 > 20.[2]
- 9.Solve 5x + 6 < 31 and list the positive integers that satisfy it (if finite).[3]
- 10.Solve 5x + 2 < 17 and list the positive integers that satisfy it (if finite).[3]
- 11.Solve 5x + 13 ≤ 33 and list the positive integers that satisfy it (if finite).[3]
- 12.Solve 5x + 15 ≤ 20 and list the positive integers that satisfy it (if finite).[3]
Show answers and working
1. x ≥ 3
Subtract 9: 3x ≥ 9. Divide by 3 (positive, so the sign stays): x ≥ 3.
2. x < 3
Subtract 7: 5x < 15. Divide by 5 (positive, so the sign stays): x < 3.
3. x > 6
Subtract 8: 4x > 24. Divide by 4 (positive, so the sign stays): x > 6.
4. x ≤ 8
Subtract 13: 3x ≤ 24. Divide by 3 (positive, so the sign stays): x ≤ 8.
5. x < 4
Subtract 8: 5x < 20. Divide by 5 (positive, so the sign stays): x < 4.
6. x > 4
Subtract 6: 2x > 8. Divide by 2 (positive, so the sign stays): x > 4.
7. x ≥ 5
Subtract 14: 6x ≥ 30. Divide by 6 (positive, so the sign stays): x ≥ 5.
8. x > 2
Subtract 8: 6x > 12. Divide by 6 (positive, so the sign stays): x > 2.
9. x < 5
Subtract 6: 5x < 25. Divide by 5 (positive, so the sign stays): x < 5.
10. x < 3
Subtract 2: 5x < 15. Divide by 5 (positive, so the sign stays): x < 3.
11. x ≤ 4
Subtract 13: 5x ≤ 20. Divide by 5 (positive, so the sign stays): x ≤ 4.
12. x ≤ 1
Subtract 15: 5x ≤ 5. Divide by 5 (positive, so the sign stays): x ≤ 1.
Worked examples
Solve 3x + 1 ≤ 10.
- Subtract 1: 3x ≤ 9.
- Divide by 3 (positive, so the sign stays): x ≤ 3.
- Answer: x ≤ 3
Solve 4x + 13 > 21.
- Subtract 13: 4x > 8.
- Divide by 4 (positive, so the sign stays): x > 2.
- Answer: x > 2
Solve 6x + 6 < 36 and list the positive integers that satisfy it (if finite).
- Subtract 6: 6x < 30.
- Divide by 6 (positive, so the sign stays): 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.
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.
Every free resource for Inequality Notation
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Learn — Meet the idea.
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Frequently asked
- Is this Grade 3 Inequality Notation 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 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 Inequality Notation?
- Move on to Solving Linear Inequalities, Inequalities on a Number Line, Algebraic Expressions, Equations, which build directly on this idea.
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