NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities thoroughly explains all the fundamentals of linear inequalities and their algebraic solutions. A statement involving less than, greater than, or equal to is known as an inequality. Thus, Linear Inequalities is a study of problems involving non-equal expressions or numbers. This topic is quite advantageous in solving various problems in the fields of science, psychology, statistics, mathematics, economics, etc.

NCERT Solutions Class 11 Maths Chapter 6 comprehensively explains all the key concepts related to Linear Inequalities with examples. Students will easily acquire detailed knowledge of this topic and its practical applications with the help of these solutions.

Two algebraic expressions or real numbers related by the symbol ≤, ≥, < and > form an inequality.

For example:

ax + by > 0, 16a – 46b < 0, etc.

Download PDF of NCERT Solutions for Class 11 Maths Chapter 6 – Linear Inequalities

NCERT Solutions for Class 11 Maths Chapter 6 – Linear Inequalities

The summary of the concepts involved in the NCERT Solutions for Class 11 Maths Chapter 6 of ANAND CLASSES’S is given below:

1. Two real numbers or two algebraic expressions related by the symbols <, >, ≤ or ≥ form an inequality.
2. Equal numbers may be added to (or subtracted from) both sides of an inequality.
3. Both sides of an inequality can be multiplied (or divided) by the same positive number. But, when both sides are multiplied (or divided) by a negative number, then the inequality is reversed.
4. The values of x, which make an inequality a true statement, are called solutions of the inequality.
5. To represent x < a (or x > a) on a number line, put a circle on the number a and dark line to the left (or right) of the number a.
6. To represent x ≤ a (or x ≥ a) on a number line, put a dark circle on the number a and darken the line to the left (or right) of the number x.
7. If inequality is having ≤ or ≥ symbol, then the points on the line are also included in the solutions of the inequality, and the graph of the inequality lies to the left (below) or right (above) of the graph of the equality represented by a dark line that satisfies an arbitrary point in that part.
8. If an inequality is having < or > symbol, then the points on the line are not included in the solutions of the inequality, and the graph of the inequality lies to the left (below) or right (above) of the graph of the corresponding equality represented by a dotted line that satisfies an arbitrary point in that part.
9. The solution region of a system of inequalities is the region which satisfies all the given inequalities in the system simultaneously.

Features of NCERT Solutions for Class 11 Maths Chapter 6 – Linear Inequalities

The solutions for NCERT questions provided by ANAND CLASSES’S for Class 11 Maths Chapter 6 have covered the below concepts. These solutions are prepared meticulously to avoid mistakes so that students are assured of getting full marks after practising them.

• Meaning of Linear inequalities.
• Algebraic solutions of linear inequalities in one variable and their representation on the number line.
• Graphical solution of linear inequalities in two variables.
• Graphical method of finding a solution of systems of linear inequalities in two variables.

Frequently Asked Questions (FAQs) on NCERT Solutions for Class 11 Maths Chapter 6

Q1

List out the number of exercises present in NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities.

The chapter consists of 3 exercises and one miscellaneous exercise which covers all the topics. The number of questions present in each exercise is mentioned below.
Exercise 6.1 – 26 Questions
Exercise 6.2 – 10 Questions
Exercise 6.3 – 15 Questions
Miscellaneous Exercise – 14 Questions

Q2

Mention the important topics covered in the NCERT Solutions for Class 11 Maths Chapter 6.

The important topics covered in the NCERT Solutions for Class 11 Maths Chapter 6 are as follows:
1. Introduction
2. Inequalities
3. Algebraic Solutions of Linear Inequalities in One Variable and Their Graphical Representation
4. Graphical Solution of Linear Inequalities in Two Variables
5. Solution of System of Linear Inequalities in Two Variables

in order to get an idea about the other methods, which can be used to solve the NCERT problems.

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