Free Grade 3 Working with Solving Linear Inequalities Worksheets
Free Grade 3 worksheets for Working with Solving Linear 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
Stretch
30 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain working with solving linear inequalities
Explain working with solving linear inequalities accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with solving linear inequalities
Calculate working with solving linear inequalities accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with solving linear inequalities
Compare working with solving linear inequalities accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify working with solving linear inequalities
Justify working with solving linear 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 Working with Solving Linear 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 4x + 3 ≤ 15.[1]
- 2.Solve 6x + 6 > 36.[1]
- 3.Solve 3x + 14 ≤ 35.[1]
- 4.Solve 6x + 13 ≥ 55.[1]
- 5.Solve 3x + 15 ≥ 18.[2]
- 6.Solve 2x + 5 < 17.[2]
- 7.Solve 2x + 7 > 23.[2]
- 8.Solve 2x + 4 > 6.[2]
- 9.Solve 4x + 13 > 25 and list the positive integers that satisfy it (if finite).[3]
- 10.Solve 6x + 11 ≤ 35 and list the positive integers that satisfy it (if finite).[3]
- 11.Solve 4x + 2 ≥ 26 and list the positive integers that satisfy it (if finite).[3]
- 12.Solve 2x + 9 > 15 and list the positive integers that satisfy it (if finite).[3]
Show answers and working
1. x ≤ 3
Subtract 3: 4x ≤ 12. Divide by 4 (positive, so the sign stays): x ≤ 3.
2. x > 5
Subtract 6: 6x > 30. Divide by 6 (positive, so the sign stays): x > 5.
3. x ≤ 7
Subtract 14: 3x ≤ 21. Divide by 3 (positive, so the sign stays): x ≤ 7.
4. x ≥ 7
Subtract 13: 6x ≥ 42. Divide by 6 (positive, so the sign stays): x ≥ 7.
5. x ≥ 1
Subtract 15: 3x ≥ 3. Divide by 3 (positive, so the sign stays): x ≥ 1.
6. x < 6
Subtract 5: 2x < 12. Divide by 2 (positive, so the sign stays): x < 6.
7. x > 8
Subtract 7: 2x > 16. Divide by 2 (positive, so the sign stays): x > 8.
8. x > 1
Subtract 4: 2x > 2. Divide by 2 (positive, so the sign stays): x > 1.
9. x > 3
Subtract 13: 4x > 12. Divide by 4 (positive, so the sign stays): x > 3.
10. x ≤ 4
Subtract 11: 6x ≤ 24. Divide by 6 (positive, so the sign stays): x ≤ 4.
11. x ≥ 6
Subtract 2: 4x ≥ 24. Divide by 4 (positive, so the sign stays): x ≥ 6.
12. x > 3
Subtract 9: 2x > 6. Divide by 2 (positive, so the sign stays): x > 3.
Worked examples
Solve 3x + 8 > 29.
- Subtract 8: 3x > 21.
- Divide by 3 (positive, so the sign stays): x > 7.
- Answer: x > 7
Solve 3x + 3 < 15.
- Subtract 3: 3x < 12.
- Divide by 3 (positive, so the sign stays): x < 4.
- Answer: x < 4
Solve 6x + 1 ≥ 43 and list the positive integers that satisfy it (if finite).
- Subtract 1: 6x ≥ 42.
- Divide by 6 (positive, so the sign stays): x ≥ 7.
- Answer: x ≥ 7
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 Working with Solving Linear 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 Introducing Solving Linear Inequalities, Inequality Notation. 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 Working with Solving Linear Inequalities?
- Move on to Solving Linear Inequalities in Context, Inequality Notation, Inequalities on a Number Line, which build directly on this idea.
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