**NCERT Solutions For Class 11 Maths Chapter 6 Linear Inequalities** are prepared by the highly qualified expert teachers at BYJUâ€™S. These NCERT Solutions of Maths help the students in solving the problems promptly, correctly and efficiently. The solutions for NCERT textbook questions designed by BYJUâ€™S contain steps with appropriate formulas and examples. All these solutions are written as per the latest guidelines of the examination boards to help the students in scoring full marks.

The PDF of Class 11 Maths NCERT Solutions for Chapter 6 Linear Inequalities serves as a detailed study material. BYJUâ€™S designs all the concepts, and solutions in simple words so that students can easily learn the chapter in less time. Also, NCERT Solutions of BYJUâ€™S are accurate and students need not worry about the quality and correctness of the solutions. This type of knowledge helps in gaining and remembering more concepts for their upcoming exams.

Linear Inequalities are used in many real-life applications such as income and expenditure problems to find the proportion of the amount spent on various things. Two types of linear inequalities are explained in NCERT Solutions For Class 11 Maths of Chapter 6, i.e. linear inequalities in one variable and linear inequalities in two variables.

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## NCERT Solutions for Class 11 Maths Chapter 6- Linear Inequalities

The Chapter Linear Inequalities belongs to the unit Algebra, and there exist 3 exercises and a miscellaneous exercise in this chapter, which help the students understand the concepts related to the chapter in detail. The topics covered in Chapter 6 Linear Inequalities of NCERT Solutions for Class 11 include:

**6.1 Introduction**

Two algebraic expressions or real numbers related by any of the symbols â‰¤, â‰¥, <, and > form an inequality. For example: px + qy > 0, 3a â€“19b < 0. Here, students will be able to know how to solve word problems by converting them into inequalities.

**6.2 Inequalities**

This topic is well explained with the real-life scenarios which can be transformed to linear inequalities. Also, enough practice problems are provided along with solved examples.

**6.3 Algebraic Solutions of Linear Inequalities in 1 Variable and their Graphical Representation**

In this exercise, students can learn the meaning of a solution of linear inequalities and the graphical representation of these solutions. Besides, the methods of finding the solutions for linear inequalities have been explained with examples.

**6.4 Graphical Solution of Linear Inequalities in Two Variables**

After this section, students can understand the representation of the solution of linear inequalities in two variables on the Cartesian plane. Also, they can identify the solution region for the given inequalities.

**6.5 Solution of System of Linear Inequalities in Two Variables**

The solution of the system of linear inequalities in two variables using graphical methods is explained with many examples to help the students to understand the concept in a better way.

Exercise 6.1 Solutions 26 Questions

Exercise 6.2 Solutions 10 Questions

Exercise 6.3 Solutions 15 Questions

Miscellaneous Exercise On Chapter 6 Solutions 14 Questions

## NCERT Solutions for Class 11 Maths Chapter 6- Linear Inequalities

The summary of the concepts involved in the NCERT Solutions of BYJUâ€™S are given below:

- Two real numbers or two algebraic expressions related by the symbols <, >, â‰¤ or â‰¥ form an inequality.
- Equal numbers may be added to (or subtracted from) both sides of an inequality.
- 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.
- The values of x, which make an inequality a true statement, are called solutions of the inequality.
- 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.
- To represent x â‰¤ a (or x â‰¥ a) on a number line, put a dark circle on the number a and dark the line to the left (or right) of the number x.
- If inequality is having â‰¤ or â‰¥ symbol, then the points on the line are also included in the solutions of the inequality and the graph of the inequality lies left (below) or right (above) of the graph of the equality represented by a dark line that satisfies an arbitrary point in that part.
- 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 dotted line that satisfies an arbitrary point in that part.
- The solution region of a system of inequalities is the region which satisfies all the given inequalities in the system simultaneously.

### Key Features of NCERT Solutions for Class 11 Maths Chapter 6- Linear Inequalities

The solutions for NCERT questions provided by BYJUâ€™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 practicing 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.