Free Grade 3 Inequalities Worksheets
Free Grade 3 worksheets for Inequalities: 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.
- RememberIdentify inequalities
Identify inequalities accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain inequalities
Explain inequalities accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate inequalities
Calculate inequalities accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare inequalities
Compare inequalities 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 Inequalities 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 + 6 ≤ 16.[1]
- 2.Solve 2x + 14 ≤ 24.[1]
- 3.Solve 6x + 6 ≥ 12.[1]
- 4.Solve 5x + 6 > 46.[1]
- 5.Solve 6x + 12 ≤ 30.[2]
- 6.Solve 6x + 1 > 7.[2]
- 7.Solve 6x + 13 < 67.[2]
- 8.Solve 4x + 9 < 17.[2]
- 9.Solve 3x + 15 ≤ 33 and list the positive integers that satisfy it (if finite).[3]
- 10.Solve 4x + 12 > 40 and list the positive integers that satisfy it (if finite).[3]
- 11.Solve 4x + 10 < 26 and list the positive integers that satisfy it (if finite).[3]
- 12.Solve 3x + 2 > 20 and list the positive integers that satisfy it (if finite).[3]
Show answers and working
1. x ≤ 2
Subtract 6: 5x ≤ 10. Divide by 5 (positive, so the sign stays): x ≤ 2.
2. x ≤ 5
Subtract 14: 2x ≤ 10. Divide by 2 (positive, so the sign stays): x ≤ 5.
3. x ≥ 1
Subtract 6: 6x ≥ 6. Divide by 6 (positive, so the sign stays): x ≥ 1.
4. x > 8
Subtract 6: 5x > 40. Divide by 5 (positive, so the sign stays): x > 8.
5. x ≤ 3
Subtract 12: 6x ≤ 18. Divide by 6 (positive, so the sign stays): x ≤ 3.
6. x > 1
Subtract 1: 6x > 6. Divide by 6 (positive, so the sign stays): x > 1.
7. x < 9
Subtract 13: 6x < 54. Divide by 6 (positive, so the sign stays): x < 9.
8. x < 2
Subtract 9: 4x < 8. Divide by 4 (positive, so the sign stays): x < 2.
9. x ≤ 6
Subtract 15: 3x ≤ 18. Divide by 3 (positive, so the sign stays): x ≤ 6.
10. x > 7
Subtract 12: 4x > 28. Divide by 4 (positive, so the sign stays): x > 7.
11. x < 4
Subtract 10: 4x < 16. Divide by 4 (positive, so the sign stays): x < 4.
12. x > 6
Subtract 2: 3x > 18. Divide by 3 (positive, so the sign stays): x > 6.
Worked examples
Solve 2x + 9 > 19.
- Subtract 9: 2x > 10.
- Divide by 2 (positive, so the sign stays): x > 5.
- Answer: x > 5
Solve 4x + 3 ≤ 7.
- Subtract 3: 4x ≤ 4.
- Divide by 4 (positive, so the sign stays): x ≤ 1.
- Answer: x ≤ 1
Solve 5x + 11 < 21 and list the positive integers that satisfy it (if finite).
- Subtract 11: 5x < 10.
- Divide by 5 (positive, so the sign stays): x < 2.
- Answer: x < 2
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 Inequalities
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Learn — Meet the idea.
Practice — Build fluency.
Revise — Keep it in memory.
Assess — Prove mastery.
Apply — Use it in context.
Teach — Deliver it to a class.
Frequently asked
- Is this Grade 3 Inequalities 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 Equations, Algebraic Expressions, Number Sense. 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 Inequalities?
- Move on to Sequences, Quadratics, Simultaneous Equations, Functions, which build directly on this idea.
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