# NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities

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.

In real life, we come across many such situations where a non-equal comparison is made between two mathematical expressions or two numbers. For example, the weight of all the students in your class is less than 60 kg, or the occupancy of a classroom is at most 60 desks. In all these cases, we notice that the relationship involved among the pairs of quantities is less than, less than, greater than, or equal. Thus, learning Linear Inequalities is crucial for maths and holds great importance in understanding other topics as well. NCERT Solutions Class 11 Maths Chapter 6 will deliver deep knowledge of necessary concepts based on Linear Inequalities. To learn and practice with NCERT Solutions Chapter 6 Linear Inequalities, download the exercises provided in the links below.

- NCERT Solutions Class 11 Maths Chapter 6 Ex 6.1
- NCERT Solutions Class 11 Maths Chapter 6 Ex 6.2
- NCERT Solutions Class 11 Maths Chapter 6 Ex 6.3
- NCERT Solutions Class 11 Maths Chapter 6 Miscellaneous Exercise

## NCERT Solutions for Class 11 Maths Chapter 6 PDF

Linear inequalities deal with the study of expressions that involve comparing any two values by an inequality symbol such as, ‘<’, ‘>’, ‘≤’ or ‘≥’. The compared values can be numerical, algebraic, or a combination of both. NCERT Solutions for Class 11 Maths Chapter 6 are well-framed resources that support in-depth learning of such expressions and their applications. There are definitions, theorems, practical problems, and examples provided in this chapter that will aid in memorizing the concepts better. Thus, practicing and learning this chapter will ensure a better exam score. To learn with these solutions, click on the links of the pdf files given below.

**ā** Download Class 11 Maths NCERT Solutions Chapter 6 Linear Inequalities

**NCERT Class 11 Maths Chapter 6 **

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

The topic of linear inequalities and their application are well explained in these solutions with the help of illustrations. NCERT solutions Class 11 Maths Chapter 6 Linear Inequalities offer holistic learning and development to strengthen cognitive skills. The format of these solutions is prominent in imparting a clear and accurate knowledge of the subject. The details of each topic are covered efficiently to help students gain a thorough understanding as well as the required skills to successfully solve all problems. To practice the exercise-wise NCERT Solutions Class 11 Maths Linear Inequalities, try the links given below.

- Class 11 Maths Chapter 6 Ex 6.1 - 26 Questions
- Class 11 Maths Chapter 6 Ex 6.2 - 10 Questions
- Class 11 Maths Chapter 6 Ex 6.3 - 14 Questions
- Class 11 Maths Chapter 6 Miscellaneous Ex - 15 Questions

ā Download Class 11 Maths Chapter 6 NCERT Book

**Topics Covered:** The important topics covered in NCERT solutions Class 11 Maths Chapter 6 are an introduction to linear inequalities, algebraic solutions of linear inequalities in one variable, their graphical representation, graphical solution of linear inequalities in two variables, and solution of the system of linear inequalities in two variables.

**Total Questions:** Class 11 Maths Chapter 6 Linear Inequalities has a total of 50 questions in 3 exercises, including 15 problems in a miscellaneous exercise. The problems provided in these exercises are primarily based on the understanding of linear inequalities, their algebraic solutions, and graphical representation.

## List of Formulas in NCERT Solutions Class 11 Maths Chapter 6

Gaining knowledge of all important terms and formulas is necessary for finding solutions to linear inequalities in one variable and two variables. NCERT Solutions Class 11 Maths Chapter 6 will enable students to grasp all important concepts with the help of well-elaborated examples. This chapter sees the use of a child’s acumen as well as graphical interpretations to get the solutions to various questions. Rather than formulas, there are certain rules that kids need to remember before attempting the problems in this chapter. Each concept in these solutions is detailed to impart in-depth knowledge of Linear Inequalities. Some of the important terms, formulas, and concepts explained in these solutions are listed below:

- Two real numbers or two algebraic expressions related by the symbol

‘<’, ‘>’, ‘≤’ or ‘≥’ form an inequality.

**Addition Rule of Linear Inequalities:**The addition property of inequality says that adding the same number to each side of the inequality produces an equivalent inequality.

I.e., If x > y ,then x + z > y+z and if x < y, then x + z < y + z

**Subtraction Rule of Linear Inequalities:**The subtraction property of inequality says subtracting the same number from both sides of an inequality gives an equivalent inequality.

If x > y, then x − z > y − z

If x< y, then x − z < y − z

**Multiplication Rule of Linear Inequalities:**The multiplication property of inequality tells us that multiplication on both sides of an inequality with a positive number produces an equivalent inequality.

If x> y and z > 0, then xz > yz

If x<y and z > 0, then xz < yz

**Division Rule of Linear Inequalities:**Division of both sides of an inequality with a positive number produces an equivalent inequality.

If x > y and z > 0, then x/z > y/z

If x < y and z > 0, then x/z < y/z

## FAQs on NCERT Solutions Class 11 Maths Chapter 6

### What is the Importance of NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities?

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities are prepared by a team of experienced teachers and math experts after deep research to help students relate the linear inequalities concepts to real-life issues. The questions and examples provided in these solutions are highly proficient in delivering a clear knowledge of linear inequalities in algebra and their solutions. The well-structured format of these solutions is efficient in creating a solid foundation for understanding complex topics. Plenty of examples and sample questions explained in a lucid manner are suitable to provide in-depth learning of each topic. Thus, these solutions are perfect study material for excelling in exams.

### What are the Important Topics Covered in Class 11 Maths NCERT Solutions Chapter 6?

NCERT Solutions Class 11 Maths Chapter 6 starts with a brief introduction to linear inequalities and terms related to them. It also covers some of the most important algebraic concepts of solving linear inequalities in one and two variables along with their graphical representation. With the thorough practice of these solutions, students can easily understand the meaning of linear inequalities, their algebraic solutions, and their representation on the number line.

### Do I Need to Practice all Questions Provided in NCERT Solutions Class 11 Maths Linear Inequalities?

The questions provided in the NCERT Solutions Class 11 Maths Linear Inequalities are competent to promote the learning of key concepts. With regular practice of these problems, students will attain the core fundamentals to have a firm grip over facts related to Linear Inequalities. These questions enhance conceptual fluency in solving algebraic problems based on the graphical representation of linear inequalities in one and two variables.

### How Many Questions are there in Class 11 Maths NCERT Solutions Chapter 6 Linear Inequalities?

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities has 65 questions in 4 exercises. These four exercises conveniently cover the overall topic through interactive examples and practice problems. Students can easily learn the representation of linear inequalities and their graphical solutions by revising all the sums provided in these solutions. They are also helpful in enhancing the basic algebraic competency for competitive studies.

### What are the Important Formulas in NCERT Solutions Class 11 Maths Chapter 6?

NCERT Solutions Class 11 Maths Chapter 6 explains the visualization of inequalities. Some of the important formulas and concepts introduced in these solutions are based on the basic properties of addition, subtraction, multiplication, and division of linear inequalities. Apart from these, the concept of graphical and algebraic solutions of linear inequalities with one and two variables is well-elaborated. Students can form a clear base for understanding each step of the solutions with the help of pre-solved sums and examples provided before the exercises.

### Why Should I Practice Class 11 Maths NCERT Solutions Chapter 6 Linear Inequalities?

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities is a perfect resource to develop the conceptual understanding of linear inequalities and their algebraic properties. These basic concepts are highly effective in learning a step-wise approach to the whole syllabus of Class 11 Maths Chapter 6. The easy-to-understand pattern of problems incorporated in these solutions is facile to get a hold of all complex concepts with ease. Thus, practicing these solutions is essential for efficient exam preparation and to score better.