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Linear Inequalities — Revision Notes

Punjab Board · Class 11 · Mathematics

Linear Inequalities revision notes for Punjab Board Class 11 Mathematics: 4 topics in quick points. Part of the Punjab Board Class 11 Mathematics syllabus.

45 questions25 flashcards2 formulas & key relations5 concepts

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An infographic classifying different types of inequalities based on variables, symbols, and degree, including numerical, literal, strict, slack, linear in one variable, linear in two variables, and qu
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Key Topics to Revise

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1. Basic Concepts and Definitions

  • An inequality is formed when two real numbers or algebraic expressions are related by <, >, ≤, or ≥.
  • Strict inequalities use < or > (the boundary point is NOT included).
  • Slack (non-strict) inequalities use ≤ or ≥ (the boundary point IS included).
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2. Rules for Solving Linear Inequalities

  • RULE 1 (Addition/Subtraction): Equal numbers may be added to or subtracted from both sides of an inequality WITHOUT changing the inequality sign.
  • RULE 2 (Multiplication/Division by POSITIVE number): Both sides can be multiplied or divided by the same POSITIVE number WITHOUT changing the inequality sign.
  • RULE 3 — THE MOST CRITICAL RULE (Multiplication/Division by NEGATIVE number): When both sides are multiplied or divided by a NEGATIVE number, the inequality sign is REVERSED (< becomes >, ≤ becomes ≥,
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3. Solving Linear Inequalities in One Variable — Step-by-Step Methods

  • STEP 1: Simplify both sides of the inequality (expand brackets, combine like terms).
  • STEP 2: Move all variable terms to the left side and all constant terms to the right side using Rule 1.
  • STEP 3: Divide or multiply both sides to make the coefficient of the variable equal to 1, applying Rule 2 or Rule 3 as appropriate.
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4. Worked Examples — One Variable Inequalities

  • EXAMPLE 1: Solve 5x - 3 < 3x + 1 when (i) x is an integer, (ii) x is a real number.
  • Step 1: 5x - 3 < 3x + 1
  • Step 2: 5x - 3x < 1 + 3 → 2x < 4 → x < 2

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Full Notes

Key Concepts

An inequality is a mathematical statementStrict inequalities use < or >You can add or subtractWhen multiplying or dividing both sidesThese are inequalities of the form

Frequently Asked Questions

What are the important topics in Linear Inequalities for Punjab Board Class 11 Mathematics?
Key topics in Linear Inequalities include Basic Concepts and Definitions, Rules for Solving Linear Inequalities, Solving Linear Inequalities in One Variable — Step-by-Step Methods, Worked Examples — One Variable Inequalities. Study these first, then practise questions on each for Class 11 exams.
How should I revise Linear Inequalities for Class 11 exams?
Learn the core ideas first, then work through the 45 practice questions on Linear Inequalities. Revise definitions regularly and use flashcards for quick recall before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

More resources for Linear Inequalities

All Punjab Board Class 11 Mathematics Revision Notes

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