NCERT Solutions Class 11 Maths Chapter 5 guides you through Linear Inequalities with detailed solutions for all 26 exercise questions. You’ll learn how to solve linear inequalities algebraically, represent solutions on number lines, solve systems of inequalities graphically, and identify solution regions in two variables. These skills are essential for optimization problems in calculus and real-world applications like resource allocation and profit maximization.
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All exercises with step-by-step solutions | Updated 2025-26 | Free Download
Download PDF (Free)NCERT Solutions Class 11 Maths Chapter 5 Linear Inequalities – Complete Guide
NCERT Class 11 Chapter 5 – Linear Inequalities introduces you to a powerful mathematical tool that goes beyond simple equations. While equations show equality, inequalities help you understand ranges and limitations in real-world scenarios. You’ll explore how to solve linear inequalities in one variable using algebraic methods and represent their solutions on number lines, then advance to two-variable inequalities with graphical representations on coordinate planes.
📊 CBSE Class 11 Maths Chapter 5 – Exam Weightage & Marking Scheme
| CBSE Board Marks | 5 Marks |
| Unit Name | Algebra |
| Difficulty Level | Medium |
| Importance | Medium |
| Exam Types | CBSE Board, State Boards |
| Typical Questions | 1-2 questions |
This chapter is crucial for CBSE board exams, carrying approximately 5 marks and featuring medium-difficulty questions. You’ll encounter various question types including 2-mark problems on solving basic inequalities, 3-mark questions on graphical representations, and 4-mark application-based problems. The chapter builds directly on your knowledge of linear equations from Class 10 and lays the foundation for Linear Programming in Class 12, making it an essential bridge topic.
You’ll discover practical applications of inequalities in everyday situations like budget constraints, profit maximization, diet planning, and resource allocation. The graphical method you learn here will help you visualize solution regions and understand feasible solutions in optimization problems. You’ll also master important concepts like strict inequalities (< and >) versus non-strict inequalities (≤ and ≥), and learn why certain operations reverse inequality signs.
Quick Facts – Class 11 Chapter 5
| 📖 Chapter Number | Chapter 5 |
| 📚 Chapter Name | Linear Inequalities |
| ✏️ Total Exercises | 1 Exercises |
| ❓ Total Questions | 26 Questions |
| 📅 Updated For | CBSE Session 2025-26 |
By mastering NCERT Class 11 Chapter 5 Linear Inequalities solutions, you’ll develop critical thinking skills for analyzing constraints and making optimal decisions. The chapter includes numerous solved examples and exercise problems that progressively build your confidence, from simple one-variable inequalities to complex systems involving multiple constraints, preparing you thoroughly for both board exams and competitive entrance tests.
NCERT Solutions Class 11 Maths Chapter 5 – All Exercises PDF Download
Download exercise-wise NCERT Solutions PDFs for offline study
| Exercise No. | Topics Covered | Download PDF |
|---|---|---|
| EXERCISE 5.1 | Complete step-by-step solutions for 26 questions | 📥 Download PDF |
Linear Inequalities – Key Formulas & Concepts
Quick reference for CBSE exams
| Formula | Description | When to Use |
|---|---|---|
| Basic Inequality Properties (Addition) If \(a < b\), then \(a + c < b + c\) | Adding the same number to both sides of an inequality doesn’t change the inequality sign. Note: This also holds true for subtraction (adding a negative number). | Isolating a variable in a linear inequality. |
| Basic Inequality Properties (Multiplication – Positive Number) If \(a < b\) and \(c > 0\), then \(ac < bc\) | Multiplying both sides of an inequality by a positive number doesn’t change the inequality sign. Note: Important! Make sure the number you’re multiplying by is positive. | Isolating a variable when its coefficient is positive. |
| Basic Inequality Properties (Multiplication – Negative Number) If \(a < b\) and \(c < 0\), then \(ac > bc\) | Multiplying both sides of an inequality by a negative number REVERSES the inequality sign. Note: This is a VERY common mistake. Always remember to flip the sign when multiplying or dividing by a negative number. | Isolating a variable when its coefficient is negative. |
| Transitive Property If \(a < b\) and \(b < c\), then \(a < c\) | If one number is less than another, and that number is less than a third, then the first number is less than the third. Note: Also applies to \(>\), \(\leq\), and \(\geq\). | Simplifying a chain of inequalities. |
| Reciprocal Property (Positive Numbers) If \(0 < a < b\), then \(\frac{1}{a} > \frac{1}{b}\) | Taking the reciprocal of positive numbers reverses the inequality. Note: Both numbers MUST be positive for this to work. | When dealing with inequalities involving reciprocals of positive numbers. |
| Reciprocal Property (Negative Numbers) If \(a < b < 0\), then \(\frac{1}{a} > \frac{1}{b}\) | Taking the reciprocal of negative numbers reverses the inequality. Note: Both numbers MUST be negative for this to work. | When dealing with inequalities involving reciprocals of negative numbers. |
| Solution Set Representation (Interval Notation) \(x \in (a, b)\) | Represents all values of x between a and b, but NOT including a and b. Note: Use parentheses () when the endpoints are NOT included. | Writing the solution to an inequality where the endpoints are not included. |
| Solution Set Representation (Closed Interval Notation) \(x \in [a, b]\) | Represents all values of x between a and b, including a and b. Note: Use brackets [] when the endpoints ARE included. | Writing the solution to an inequality where the endpoints are included. |
| Solution Set Representation (Half-Open Interval Notation) \(x \in (a, b]\) or \(x \in [a, b)\) | Represents all values of x between a and b, including one endpoint but not the other. Note: Pay attention to which endpoint is included and use the correct bracket/parenthesis. | Writing the solution to an inequality where one endpoint is included and the other is not. |
| Solving System of Inequalities Solve each inequality separately, then find the intersection of the solution sets. | To solve a system of linear inequalities, you must find the common region satisfying all inequalities. Note: Graphing the inequalities can be very helpful to visualize the common region. | When you have two or more inequalities to solve simultaneously. |
| Representing Solution on Number Line Use an open circle (o) for \(<\) or \(>\), and a closed circle (●) for \(\leq\) or \(\geq\). | Visual representation of inequality on a number line. Note: Always draw the number line and mark the critical points clearly. | Illustrating the solution set of a linear inequality. |
Frequently Asked Questions – NCERT Class 11 Maths Chapter 5
📚 Related Study Materials – Class 11 Maths Resources
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