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Linear Inequalities

Madhya Pradesh Board · Class 11 · Mathematics

Complete topic list for Linear Inequalities in Madhya Pradesh Board Class 11 Mathematics. Key concepts, sub-topics, and what to focus on for board exams.

168 questions50 flashcards5 concepts

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4 Topics · Madhya Pradesh Board Class 11 Mathematics

Topics in Linear Inequalities

1

1. Core Ideas and Types of Inequalities

  • An inequality is formed when two real numbers or two algebraic expressions are related by <, >, ≤, or ≥.
  • Examples of numerical inequalities: 3 < 5 and 7 > 5.
  • Examples of literal inequalities: x < 5, y > 2, x ≥ 3, y ≤ 4.
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2. Rules for Solving Inequalities

  • Equal numbers may be added to or subtracted from both sides of an inequality without affecting the sign of inequality.
  • Both sides of an inequality can be multiplied or divided by the same positive number.
  • When both sides are multiplied or divided by a negative number, the inequality sign reverses.
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3. Solving Linear Inequalities in One Variable

  • Start by simplifying both sides.
  • Move variable terms to one side and constants to the other using addition or subtraction.
  • If needed, divide by the coefficient of the variable.
4

4. Word Problems and Applications

  • Translate the statement into an inequality before solving.
  • Ravi’s spending leads to 30x < 200 because he buys only rice packets.
  • The solution set of 30x < 200 by trial and error over the given values is {0,1,2,3,4,5,6}.

Key Concepts

Central concept: Linear inequalities as statements comparing real numbers or algebraic expressions using <, >, ≤, or ≥, solved mainly by preserving or reversing inequality signs under allowed operations and represented on a number line

InequalityStrict inequalitySlack inequalityLinear inequality in one variableLinear inequality in two variablesQuadratic inequalitySolution of an inequalityRules for solving inequalities

Frequently Asked Questions

What are the important topics in Linear Inequalities for Madhya Pradesh Board Class 11 Mathematics?
Linear Inequalities covers several key topics that are frequently asked in Madhya Pradesh Board Class 11 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
How to score full marks in Linear Inequalities — Madhya Pradesh Board Class 11 Mathematics?
Understand the core concepts first, then work through the 168 practice questions available for this chapter. Revise formulas and 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 14 chapters — Madhya Pradesh Board Class 11 Mathematics Syllabus

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