Free Grade 3 Introducing Inequalities on a Number Line Quizzes
Free Grade 3 quizzes for Introducing Inequalities on a Number Line: 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 inequalities on a number line
Explain introducing inequalities on a number line accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing inequalities on a number line
Calculate introducing inequalities on a number line accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing inequalities on a number line
Compare introducing inequalities on a number line accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify introducing inequalities on a number line
Justify introducing inequalities on a number line 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 Inequalities on a Number Line 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 2x + 5 ≥ 23.[1]
- 2.Solve 5x + 5 < 35.[1]
- 3.Solve 6x + 9 > 51.[1]
- 4.Solve 5x + 8 ≥ 48.[1]
- 5.Solve 4x + 12 ≥ 20.[2]
- 6.Solve 3x + 5 ≥ 11.[2]
- 7.Solve 2x + 11 > 13.[2]
- 8.Solve 5x + 7 > 27.[2]
- 9.Solve 5x + 5 ≥ 45 and list the positive integers that satisfy it (if finite).[3]
- 10.Solve 5x + 2 > 12 and list the positive integers that satisfy it (if finite).[3]
- 11.Solve 3x + 4 < 16 and list the positive integers that satisfy it (if finite).[3]
- 12.Solve 5x + 8 ≥ 13 and list the positive integers that satisfy it (if finite).[3]
Show answers and working
1. x ≥ 9
Subtract 5: 2x ≥ 18. Divide by 2 (positive, so the sign stays): x ≥ 9.
2. x < 6
Subtract 5: 5x < 30. Divide by 5 (positive, so the sign stays): x < 6.
3. x > 7
Subtract 9: 6x > 42. Divide by 6 (positive, so the sign stays): x > 7.
4. x ≥ 8
Subtract 8: 5x ≥ 40. Divide by 5 (positive, so the sign stays): x ≥ 8.
5. x ≥ 2
Subtract 12: 4x ≥ 8. Divide by 4 (positive, so the sign stays): x ≥ 2.
6. x ≥ 2
Subtract 5: 3x ≥ 6. Divide by 3 (positive, so the sign stays): x ≥ 2.
7. x > 1
Subtract 11: 2x > 2. Divide by 2 (positive, so the sign stays): x > 1.
8. x > 4
Subtract 7: 5x > 20. Divide by 5 (positive, so the sign stays): x > 4.
9. x ≥ 8
Subtract 5: 5x ≥ 40. Divide by 5 (positive, so the sign stays): x ≥ 8.
10. x > 2
Subtract 2: 5x > 10. Divide by 5 (positive, so the sign stays): x > 2.
11. x < 4
Subtract 4: 3x < 12. Divide by 3 (positive, so the sign stays): x < 4.
12. x ≥ 1
Subtract 8: 5x ≥ 5. Divide by 5 (positive, so the sign stays): x ≥ 1.
Worked examples
Solve 6x + 11 ≤ 47.
- Subtract 11: 6x ≤ 36.
- Divide by 6 (positive, so the sign stays): x ≤ 6.
- Answer: x ≤ 6
Solve 2x + 10 > 12.
- Subtract 10: 2x > 2.
- Divide by 2 (positive, so the sign stays): x > 1.
- Answer: x > 1
Solve 6x + 5 < 23 and list the positive integers that satisfy it (if finite).
- Subtract 5: 6x < 18.
- Divide by 6 (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 Inequalities on a Number Line 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 Solving Linear Inequalities. 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 Inequalities on a Number Line?
- Move on to Working with Inequalities on a Number Line, Inequalities on a Number Line in Context, Inequality Notation, Solving Linear Inequalities, which build directly on this idea.
Related resources
- Free Introducing Inequalities on a Number Line worksheets
- Free Introducing Inequalities on a Number Line flashcards
- Free Introducing Inequalities on a Number Line lessons
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