Class 11 Mathematics — Chapter 5: LINEAR INEQUALITIES
Chapter 5: LINEAR INEQUALITIES is a chapter in Class 11 Mathematics (NCERT), part of the CBSE NCERT curriculum followed by over 25 million students across India. This chapter covers 7 topics including Introduction to Inequalities, Types of Linear Inequalities, Solution of an Inequality. BrainWeave provides free AI-powered explanations — by voice or text, in Hindi or English — with no signup required.
What you'll learn
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▸Introduction to Inequalitiesinequalitystrict inequalityslack inequalityinequality symbols
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▸Types of Linear Inequalitiesone variabletwo variableslinearliteral inequalities
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▸Solution of an InequalityCore conceptsolution settrue statementdomainreplacement set
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▸Rules for Solving Linear InequalitiesCore conceptalgebraic solutionreverse inequality signnegative multiplicationisolate variable
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▸Algebraic Solution of Linear Inequalities in One VariableCore conceptsolve for xinterval notationone-variable inequalitysolution interval
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▸Graphical Representation of Solutions on a Number LineCore conceptnumber linegraphical representationopen circleclosed circle
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▸Word Problems involving Linear Inequalitiesword problemsat leastat mostconsecutive numbers
Chapter Summary
Understanding the definition of an inequality, the meaning of symbols (<, >, ≤, ≥), and the difference between strict (e.g., ax + b < 0) and slack (e.g., ax + b ≤ 0) inequalities.
Differentiating between linear inequalities in one variable (e.g., ax + b > 0) and two variables (e.g., ax + by > c), and distinguishing them from non-linear inequalities like quadratic ones.
Understanding that a solution is a value of the variable that makes the inequality a true statement, and that the collection of all solutions forms the solution set. Recognizing that solutions can be considered for different sets of numbers (natural numbers, integers, real numbers).
Mastering the algebraic rules for manipulating inequalities. This includes adding/subtracting numbers and multiplying/dividing by positive numbers, with special attention to the critical rule of reversing the inequality sign when multiplying or dividing by a negative number.
Applying the rules to systematically solve linear inequalities in one variable for 'x', and expressing the solution set using interval notation (e.g., x ∈ (–∞, 2)) for real numbers.
Visualizing the solution set of a one-variable inequality by plotting it on a number line, using an open circle for strict inequalities (<, >) and a closed/filled circle for slack inequalities (≤, ≥).
Translating real-world statement problems into mathematical inequalities and solving them. This includes problems related to averages, consecutive numbers, and constraints like 'at least' or 'at most'.
Practice Questions from this Chapter
Tap "Get Solution" on any question to ask our AI tutor.
- Explain real-world inequalities simply. Get Solution →
- Show inequalities on a number line. Get Solution →
- Give more inequality solving rules. Get Solution →
- According to the text, which of the following best defines an inequality? Get Solution →
- Which of the following is an example of a 'strict inequality' as described in the chapter? Get Solution →
- The inequality `ax + b ≥ 0` is an example of which type of inequality? Get Solution →
- What is the key difference mentioned in the text for solving an inequality compared to an equation? Get Solution →
- Based on the examples on page 2, which of the following is a 'literal inequality'? Get Solution →
Did you know?
- 💡 The symbols "<" and ">" were first used by English mathematician Thomas Harriot in 1631.
- 💡 The letter "x" became popular for unknowns because Arabic texts used a sound like "sh" for it.
- 💡 Speed limits are a real-world example of inequalities, meaning you must drive less than a set speed.
- 💡 Computer programs often use inequalities to make decisions, like if a score is greater than 100.
- 💡 There are more numbers between zero and one than there are whole numbers in existence.
Frequently Asked Questions
How many topics are covered in this chapter?
This chapter covers 7 key topics: Introduction to Inequalities, Types of Linear Inequalities, Solution of an Inequality, Rules for Solving Linear Inequalities, Algebraic Solution of Linear Inequalities in One Variable, and more. The BrainWeave AI tutor explains each one with examples.
Is Chapter 5: LINEAR INEQUALITIES important for board exams?
Class 11 is a foundation year. Mastering this chapter now will help you build strong fundamentals for the higher classes.
Can I get NCERT solutions for this chapter in Hindi?
Yes. BrainWeave's AI tutor supports Hindi, English, and Hinglish for both voice and text chat. Just ask your question in your preferred language.
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