Free Grade 3 Inequality Notation in Context Worksheets
Free Grade 3 worksheets for Inequality Notation in Context: 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
Foundation
20 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify inequality notation in context
Identify inequality notation in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain inequality notation in context
Explain inequality notation in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate inequality notation in context
Calculate inequality notation in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare inequality notation in context
Compare inequality notation in context 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 in Context 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 6x + 5 ≤ 41.[1]
- 2.Solve 3x + 1 ≥ 19.[1]
- 3.Solve 6x + 8 < 20.[1]
- 4.Solve 3x + 9 ≥ 18.[1]
- 5.Solve 2x + 11 > 29.[2]
- 6.Solve 3x + 7 ≥ 31.[2]
- 7.Solve 5x + 2 < 32.[2]
- 8.Solve 3x + 7 > 22.[2]
- 9.Solve 2x + 5 ≥ 21 and list the positive integers that satisfy it (if finite).[3]
- 10.Solve 4x + 4 > 16 and list the positive integers that satisfy it (if finite).[3]
- 11.Solve 3x + 10 > 28 and list the positive integers that satisfy it (if finite).[3]
- 12.Solve 2x + 11 ≤ 27 and list the positive integers that satisfy it (if finite).[3]
Show answers and working
1. x ≤ 6
Subtract 5: 6x ≤ 36. Divide by 6 (positive, so the sign stays): x ≤ 6.
2. x ≥ 6
Subtract 1: 3x ≥ 18. Divide by 3 (positive, so the sign stays): x ≥ 6.
3. x < 2
Subtract 8: 6x < 12. Divide by 6 (positive, so the sign stays): x < 2.
4. x ≥ 3
Subtract 9: 3x ≥ 9. Divide by 3 (positive, so the sign stays): x ≥ 3.
5. x > 9
Subtract 11: 2x > 18. Divide by 2 (positive, so the sign stays): x > 9.
6. x ≥ 8
Subtract 7: 3x ≥ 24. Divide by 3 (positive, so the sign stays): x ≥ 8.
7. x < 6
Subtract 2: 5x < 30. Divide by 5 (positive, so the sign stays): x < 6.
8. x > 5
Subtract 7: 3x > 15. Divide by 3 (positive, so the sign stays): x > 5.
9. x ≥ 8
Subtract 5: 2x ≥ 16. Divide by 2 (positive, so the sign stays): x ≥ 8.
10. x > 3
Subtract 4: 4x > 12. Divide by 4 (positive, so the sign stays): x > 3.
11. x > 6
Subtract 10: 3x > 18. Divide by 3 (positive, so the sign stays): x > 6.
12. x ≤ 8
Subtract 11: 2x ≤ 16. Divide by 2 (positive, so the sign stays): x ≤ 8.
Worked examples
Solve 6x + 15 > 39.
- Subtract 15: 6x > 24.
- Divide by 6 (positive, so the sign stays): x > 4.
- Answer: x > 4
Solve 5x + 11 > 26.
- Subtract 11: 5x > 15.
- Divide by 5 (positive, so the sign stays): x > 3.
- Answer: x > 3
Solve 5x + 9 ≥ 29 and list the positive integers that satisfy it (if finite).
- Subtract 9: 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 Inequality Notation in Context worksheet really free?
- Yes. Every worksheets 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 Working with Inequality Notation, Introducing Inequality Notation, Equations. Each one has its own free lesson, worksheet and quiz.
- How is the worksheet 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 in Context?
- Move on to Solving Linear Inequalities, Inequalities on a Number Line, which build directly on this idea.
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