Free Grade 3 Introducing Inequality Notation Quizzes
Free Grade 3 quizzes for Introducing 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 introducing inequality notation
Explain introducing inequality notation accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing inequality notation
Calculate introducing inequality notation accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing inequality notation
Compare introducing inequality notation accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify introducing inequality notation
Justify introducing 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 Introducing 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 + 4 ≤ 7.[1]
- 2.Solve 4x + 1 ≤ 13.[1]
- 3.Solve 2x + 10 ≥ 18.[1]
- 4.Solve 2x + 6 > 12.[1]
- 5.Solve 6x + 1 < 13.[2]
- 6.Solve 3x + 6 ≤ 12.[2]
- 7.Solve 3x + 14 > 38.[2]
- 8.Solve 3x + 3 < 27.[2]
- 9.Solve 4x + 11 ≤ 27 and list the positive integers that satisfy it (if finite).[3]
- 10.Solve 3x + 13 < 16 and list the positive integers that satisfy it (if finite).[3]
- 11.Solve 6x + 5 < 59 and list the positive integers that satisfy it (if finite).[3]
- 12.Solve 2x + 9 ≤ 23 and list the positive integers that satisfy it (if finite).[3]
Show answers and working
1. x ≤ 1
Subtract 4: 3x ≤ 3. Divide by 3 (positive, so the sign stays): x ≤ 1.
2. x ≤ 3
Subtract 1: 4x ≤ 12. Divide by 4 (positive, so the sign stays): x ≤ 3.
3. x ≥ 4
Subtract 10: 2x ≥ 8. Divide by 2 (positive, so the sign stays): x ≥ 4.
4. x > 3
Subtract 6: 2x > 6. Divide by 2 (positive, so the sign stays): x > 3.
5. x < 2
Subtract 1: 6x < 12. Divide by 6 (positive, so the sign stays): x < 2.
6. x ≤ 2
Subtract 6: 3x ≤ 6. Divide by 3 (positive, so the sign stays): x ≤ 2.
7. x > 8
Subtract 14: 3x > 24. Divide by 3 (positive, so the sign stays): x > 8.
8. x < 8
Subtract 3: 3x < 24. Divide by 3 (positive, so the sign stays): x < 8.
9. x ≤ 4
Subtract 11: 4x ≤ 16. Divide by 4 (positive, so the sign stays): x ≤ 4.
10. x < 1
Subtract 13: 3x < 3. Divide by 3 (positive, so the sign stays): x < 1.
11. x < 9
Subtract 5: 6x < 54. Divide by 6 (positive, so the sign stays): x < 9.
12. x ≤ 7
Subtract 9: 2x ≤ 14. Divide by 2 (positive, so the sign stays): x ≤ 7.
Worked examples
Solve 4x + 9 ≥ 45.
- Subtract 9: 4x ≥ 36.
- Divide by 4 (positive, so the sign stays): x ≥ 9.
- Answer: x ≥ 9
Solve 3x + 5 ≤ 14.
- Subtract 5: 3x ≤ 9.
- Divide by 3 (positive, so the sign stays): x ≤ 3.
- Answer: x ≤ 3
Solve 3x + 10 ≤ 19 and list the positive integers that satisfy it (if finite).
- Subtract 10: 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 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?
- Move on to Working with Inequality Notation, Inequality Notation in Context, Solving Linear Inequalities, Inequalities on a Number Line, which build directly on this idea.
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