Free Grade 3 Solving Linear Inequalities Lesson Plans
Free Grade 3 lesson plans for 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
Core
25 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain solving linear inequalities
Explain solving linear inequalities accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate solving linear inequalities
Calculate solving linear inequalities accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare solving linear inequalities
Compare solving linear inequalities accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify solving linear inequalities
Justify 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 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 6x + 13 ≥ 31.[1]
- 2.Solve 3x + 12 < 21.[1]
- 3.Solve 6x + 5 ≥ 47.[1]
- 4.Solve 2x + 6 ≥ 10.[1]
- 5.Solve 5x + 10 ≤ 30.[2]
- 6.Solve 5x + 12 ≥ 52.[2]
- 7.Solve 5x + 2 < 17.[2]
- 8.Solve 6x + 4 < 10.[2]
- 9.Solve 4x + 3 < 35 and list the positive integers that satisfy it (if finite).[3]
- 10.Solve 2x + 5 < 11 and list the positive integers that satisfy it (if finite).[3]
- 11.Solve 5x + 8 > 43 and list the positive integers that satisfy it (if finite).[3]
- 12.Solve 6x + 15 < 21 and list the positive integers that satisfy it (if finite).[3]
Show answers and working
1. x ≥ 3
Subtract 13: 6x ≥ 18. Divide by 6 (positive, so the sign stays): x ≥ 3.
2. x < 3
Subtract 12: 3x < 9. Divide by 3 (positive, so the sign stays): x < 3.
3. x ≥ 7
Subtract 5: 6x ≥ 42. Divide by 6 (positive, so the sign stays): x ≥ 7.
4. x ≥ 2
Subtract 6: 2x ≥ 4. Divide by 2 (positive, so the sign stays): x ≥ 2.
5. x ≤ 4
Subtract 10: 5x ≤ 20. Divide by 5 (positive, so the sign stays): x ≤ 4.
6. x ≥ 8
Subtract 12: 5x ≥ 40. Divide by 5 (positive, so the sign stays): x ≥ 8.
7. x < 3
Subtract 2: 5x < 15. Divide by 5 (positive, so the sign stays): x < 3.
8. x < 1
Subtract 4: 6x < 6. Divide by 6 (positive, so the sign stays): x < 1.
9. x < 8
Subtract 3: 4x < 32. Divide by 4 (positive, so the sign stays): x < 8.
10. x < 3
Subtract 5: 2x < 6. Divide by 2 (positive, so the sign stays): x < 3.
11. x > 7
Subtract 8: 5x > 35. Divide by 5 (positive, so the sign stays): x > 7.
12. x < 1
Subtract 15: 6x < 6. Divide by 6 (positive, so the sign stays): x < 1.
Worked examples
Solve 6x + 1 < 7.
- Subtract 1: 6x < 6.
- Divide by 6 (positive, so the sign stays): x < 1.
- Answer: x < 1
Solve 3x + 15 < 39.
- Subtract 15: 3x < 24.
- Divide by 3 (positive, so the sign stays): x < 8.
- Answer: x < 8
Solve 4x + 13 ≤ 25 and list the positive integers that satisfy it (if finite).
- Subtract 13: 4x ≤ 12.
- Divide by 4 (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 Solving Linear Inequalities lesson plan really free?
- Yes. Every lesson plans 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 Inequality Notation, Equations. Each one has its own free lesson, worksheet and quiz.
- How is the lesson plan 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 Solving Linear Inequalities?
- Move on to Inequalities on a Number Line, Algebraic Expressions, Equations, Sequences, which build directly on this idea.
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