# NCERT Exemplar Class 11 Maths Chapter 6 Solutions: Linear Inequalities

NCERT Exemplar Solutions for Class 11 Maths Chapter 6 prepared by the experts at Instasolv forms an integral part of the syllabus. This chapter of NCERT Exemplar Class 11 Maths mainly focuses on the solutions of inequalities. All the questions are explained well with the help of examples to help you clear your concepts. These solutions not only help you prepare for CBSE exams but also for the entrance exams like NEET, BITSAT, and JEE.

Some of the important topics of Chapter 6 – Linear Inequalities include Introduction to Inequalities and Algebraic Solutions of Linear Inequalities in one variable. There are different topics in the chapter such as the graphical solution of linear inequalities in two variables and the solution of a system of linear inequalities in two variables worth paying attention to preparing the whole chapter.

Chapter 6 of class 11 maths NCERT Exemplar book consists of 4 exercises with a total of 32 questions. Thus, by referring to our NCERT Exemplar Solutions Chapter 6, you can prepare all the topics quite perfectly and within the right time frame.

### Important Topics for NCERT Maths Exemplar Solutions Class 11 Chapter 6 – Linear Inequalities

**What are Inequalities?**

Two real numbers or algebraic expressions that are associated with the symbols <, >, ≤ or ≥ form an inequality. For example, 4x<40 and 5x+y<32. Equal numbers may be added to or subtracted from both sides of an inequality.

**What is a Linear Inequality?**

Linear Inequality is said to be an inequality if each variable takes place in the first degree only and there is no term including the product of the variables. For example, mx + n < 0, mx + n ≤ 0, mx + ny + z > 0, and mx + ny +z ≥ 0.

**What are Closed Intervals?**

If a and b are two real numbers, where a < b, then the set of all real numbers x such that m ≤ x ≤ n is known as the closed intervals and are represented by R. Thus, [m, n] = {x: m ≤ x ≤ n, x ϵ R}.

**What are Open Intervals?**

If a and b are two real numbers, where a < b, then the set of all real numbers x such that m < x < n is known as the open intervals and are represented by (m, n) or ]m, n[. Thus, [m, n] = {x: m < x < n, x ϵ R}.

**The Solution of an Inequality**

There come to values of x, which make an inequality a true statement, those are known as the solutions of the inequality.

**Graphical Solution of Linear Inequality in Two Variables**

After documentation of the half-plane, we shade the half-planes of the inequality that is provided to us. The points of the enclosed area of the shaded portion are the solution to the given solution of the inequality.

### Exercise-wise Discussion of NCERT Maths Exemplar Solutions Class 11 Chapter 6 – Linear Inequalities

Chapter 6 – Linear Inequalities has 3 exercises with a total of 32 questions. The detailed description of these exercises is provided below:

**Exercise 6.1 – Short Answer Types Questions**

This is the first exercise of NCERT Exemplar Class 11 Maths Solutions for Chapter 6. It contains 12 short answer type questions. Practising these questions will help you clear your concepts on the solutions of inequalities.

**Exercise 6.2 – Long Answer Type Questions**

This exercise consists of a total of 6 questions based on the introduction to inequalities and algebraic solutions of linear inequalities in one variable. They are long answer type questions where you will find detailed solutions to the problems.

**Exercise 6.3 – Objective Type Questions**

Exercise 6.3 of Chapter 6 is considered a very important exercise from the entrance exam point of view. It contains a total of 14 questions including fill in the blanks, state true or false, or multiple-choice questions. Solving the questions of this exercise will help you understand how clear your concepts are.

Other than these exercises, there are a few solved examples available which you can practice to have a better understanding of the chapter.

## Why Use NCERT Maths Exemplar Solutions Class 11 Chapter 6 – Linear Inequalities by Instasolv?

- NCERT Exemplar Class 11 Chapter 6 has been prepared by Instasolv keeping in mind to solve all the complex problems of the chapter.
- Referring to these exemplar solutions will help you in your academic exam preparation and various engineering entrance exams.
- In these solutions, even the most difficult problem has been broken down to make your learning easier.
- Our experts have provided some shortcuts, important tips and tricks to help you excel in your academic score.
- Practising these solutions will help you develop a mindset that will help you in clearing tough exams with ease.