Free Grade 3 Introducing Inequality Notation Essentials Quizzes
Free Grade 3 quizzes for Introducing Inequality Notation Essentials: 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
35 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain introducing inequality notation essentials
Explain introducing inequality notation essentials accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing inequality notation essentials
Calculate introducing inequality notation essentials accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing inequality notation essentials
Compare introducing inequality notation essentials accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify introducing inequality notation essentials
Justify introducing inequality notation essentials 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 Introducing Inequality Notation Essentials 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 5x + 1 < 46.[1]
- 2.Solve 5x + 9 ≥ 39.[1]
- 3.Solve 6x + 7 < 55.[1]
- 4.Solve 2x + 14 ≤ 30.[1]
- 5.Solve 6x + 3 > 9.[2]
- 6.Solve 2x + 14 > 32.[2]
- 7.Solve 5x + 1 ≥ 26.[2]
- 8.Solve 6x + 8 < 32.[2]
- 9.Solve 6x + 15 ≥ 57 and list the positive integers that satisfy it (if finite).[3]
- 10.Solve 5x + 3 < 23 and list the positive integers that satisfy it (if finite).[3]
- 11.Solve 3x + 7 < 13 and list the positive integers that satisfy it (if finite).[3]
- 12.Solve 2x + 13 ≤ 31 and list the positive integers that satisfy it (if finite).[3]
Show answers and working
1. x < 9
Subtract 1: 5x < 45. Divide by 5 (positive, so the sign stays): x < 9.
2. x ≥ 6
Subtract 9: 5x ≥ 30. Divide by 5 (positive, so the sign stays): x ≥ 6.
3. x < 8
Subtract 7: 6x < 48. Divide by 6 (positive, so the sign stays): x < 8.
4. x ≤ 8
Subtract 14: 2x ≤ 16. Divide by 2 (positive, so the sign stays): x ≤ 8.
5. x > 1
Subtract 3: 6x > 6. Divide by 6 (positive, so the sign stays): x > 1.
6. x > 9
Subtract 14: 2x > 18. Divide by 2 (positive, so the sign stays): x > 9.
7. x ≥ 5
Subtract 1: 5x ≥ 25. Divide by 5 (positive, so the sign stays): x ≥ 5.
8. x < 4
Subtract 8: 6x < 24. Divide by 6 (positive, so the sign stays): x < 4.
9. x ≥ 7
Subtract 15: 6x ≥ 42. Divide by 6 (positive, so the sign stays): x ≥ 7.
10. x < 4
Subtract 3: 5x < 20. Divide by 5 (positive, so the sign stays): x < 4.
11. x < 2
Subtract 7: 3x < 6. Divide by 3 (positive, so the sign stays): x < 2.
12. x ≤ 9
Subtract 13: 2x ≤ 18. Divide by 2 (positive, so the sign stays): x ≤ 9.
Worked examples
Solve 6x + 4 ≥ 16.
- Subtract 4: 6x ≥ 12.
- Divide by 6 (positive, so the sign stays): x ≥ 2.
- Answer: x ≥ 2
Solve 6x + 1 ≤ 7.
- Subtract 1: 6x ≤ 6.
- Divide by 6 (positive, so the sign stays): x ≤ 1.
- Answer: x ≤ 1
Solve 3x + 1 < 10 and list the positive integers that satisfy it (if finite).
- Subtract 1: 3x < 9.
- Divide by 3 (positive, so the sign stays): x < 3.
- Answer: x < 3
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 Introducing Inequality Notation Essentials 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 Introducing Inequality Notation Essentials?
- Move on to Introducing Inequality Notation Techniques, Introducing Inequality Notation Word Problems, Introducing Inequality Notation Common Errors, Working with Inequality Notation, which build directly on this idea.
Related resources
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