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Linear Inequalities — Syllabus

Punjab Board · Class 11 · Mathematics

What Linear Inequalities covers in Punjab Board Class 11 Mathematics: 4 topics, for the 2026-27 session. Topics include Basic Concepts and Definitions.

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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4 Topics · Punjab Board Class 11 Mathematics · 2026-27

Topics in Linear Inequalities

1

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).
2

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

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

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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.

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All Punjab Board Class 11 Mathematics Syllabus

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