NCERT Class 11 Mathematics Mathematics: Chapter 5 — Linear Inequalities
This chapter introduces the concept of linear inequalities in one and two variables, building upon the study of equations. It explains that not all real-world situations can be represented by equations, and inequalities involving symbols like <, >, ≤, and ≥ are necessary. Examples like Ravi's rice purchase (30x < 200) and Reshma's shopping (40x + 20y ≤ 120) illustrate their application. The chapter defines inequalities, distinguishes between numerical and literal inequalities, and introduces double inequalities. It further categorizes inequalities into strict (e.g., ax + b < 0) and slack (e.g., ax + b ≤ 0) types, and identifies linear inequalities in one and two variables, differentiating them from quadratic inequalities. The focus remains on linear inequalities for further study.
Quick info
| Board | CBSE / NCERT |
|---|---|
| Class | Class 11 |
| Subject | Mathematics |
| Book | Mathematics |
| Chapter | Chapter 5 — Linear Inequalities |
| Language | English |
| PDF type | NCERT Textbook |
| Session | CBSE 2026 |
| Reading time | 4 minutes |
| Word count | 667 |
Learning outcomes
- Understand the concept of inequalities and their symbols (<, >, ≤, ≥).
- Differentiate between equations and inequalities.
- Identify and classify different types of inequalities (numerical, literal, double, strict, slack).
- Recognize linear inequalities in one and two variables.
- Understand the relevance of inequalities in real-world problem-solving.
Vocabulary
| Word | Meaning |
|---|---|
| Inequalities | Statements relating two real numbers or algebraic expressions using symbols <, >, ≤, or ≥. |
| Numerical inequalities | Inequalities involving only numbers, e.g., 3 < 5. |
| Literal inequalities | Inequalities involving variables, e.g., x < 5. |
| Double inequalities | Inequalities with two inequality signs, e.g., 3 < x < 5. |
| Strict inequalities | Inequalities using only < or > symbols, e.g., ax + b < 0. |
| Slack inequalities | Inequalities using ≤ or ≥ symbols, e.g., ax + b ≤ 0. |
| Linear inequalities in one variable | Inequalities of the form ax + b < 0 or ax + b > 0, where a ≠ 0. |
| Linear inequalities in two variables | Inequalities of the form ax + by < c or ax + by > c, where a ≠ 0, b ≠ 0. |
The complete chapter text is read in the official NCERT PDF viewer below (streamed from ncert.nic.in). This page provides NCERT Help study material — summary, vocabulary, practice questions, and FAQs — not a full reproduction of the textbook.
Read chapter online
This PDF is loaded from the official NCERT website (ncert.nic.in). Use the page buttons below to read — download is disabled on NCERT Help.
Read page by page below. PDF is streamed from the official NCERT website — no download button on this page.
Practice questions
- Give an example of a numerical inequality. Answer: 7 > 5
- Give an example of a literal inequality in one variable. Answer: y ≤ 4
- Is 40x + 20y < 120 a strict or slack inequality? Answer: Strict inequality.
- Is ax² + bx + c ≤ 0 a linear inequality? Answer: No, it is a quadratic inequality.
Practice MCQs
Q1. Which symbol represents 'less than or equal to'?
Explanation: The symbol '≤' denotes 'less than or equal to'.
Q2. Which of the following is an example of a numerical inequality?
Explanation: A numerical inequality involves only numbers, like 5 < 8.
Q3. The inequality 30x < 200 is an example of:
Explanation: It involves a single variable 'x' and a linear expression, using a strict inequality symbol.
Q4. Which type of inequality uses symbols like < or >?
Explanation: Strict inequalities use only the '<' or '>' symbols.
Q5. The inequality 40x + 20y ≤ 120 is a linear inequality in:
Explanation: The inequality contains two variables, 'x' and 'y', and is linear.
Frequently asked questions
What is an inequality in mathematics?
An inequality is a statement that relates two real numbers or algebraic expressions using symbols like < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).
What is the difference between an equation and an inequality?
An equation uses an equals sign (=) to state that two expressions are equal, while an inequality uses <, >, ≤, or ≥ to state a relationship of inequality between expressions.
What are strict inequalities?
Strict inequalities are those that use only the '<' or '>' symbols, meaning the two expressions cannot be equal.
What are slack inequalities?
Slack inequalities are those that use the '≤' or '≥' symbols, allowing the two expressions to be equal.
Give an example of a linear inequality in two variables.
An example is 2x + 3y < 5.
Why are inequalities important?
Inequalities are useful for representing situations where quantities are not exactly equal but fall within a certain range or limit, finding applications in science, economics, and statistics.
Related resources
Important topics
Topics covered
NCERT Class 11 Mathematics — Mathematics — Chapter 5 — Linear Inequalities. Verified by NCERT Help Editorial Team. Reviewed on 29 Jul 2026. Last updated 10 Aug 2026.