# RD Sharma Class 11 Chapter 15 Solutions (Linear Inequations)

RD Sharma Solutions for Class 11 Chapter 15 covers inequalities, algebraic solutions for linear inequalities in one step along with their graphical representation, the graphical solution of linear inequalities in two variables and solutions of the system of linear equations in two variables. This chapter is similar to Linear Inequality with Linear Equations where the equal sign is replaced by the inequality sign. Most of the questions in this chapter are based on the concept of two algebraic equations and real numbers. In CBSE exam, you can be asked a question of linear inequality with one or two variables, thus it is important to understand and learn this chapter properly.

RD Sharma Class 11 Chapter 15 contains 8 exercises with a total number of questions being 122. The difficulty level of all questions is not the same. Some of them are quite simple, whereas other questions might be difficult to solve through using simple methods and procedures. To empower your knowledge to solve these equations, you need a clear foundation of natural numbers, real numbers and integers. The short question in linear inequalities demands you to choose between less than <=, equal =, >= sign.

RD Sharma Solutions for Class 11 Chapter 15 ‘Linear Inequations’ aid in learning every topic in an easy way. It provides stepwise solutions to give a clear idea about the topic. Instasolv has identified the most probable doubts in the context of linear inequalities and devised solutions to every problem. The solutions of the RD Sharma questions are resolved with detailed explanations in a manner that you can get good practice to solve the complex questions with ease.

## Important Topics for RD Sharma Solutions for Class 11 Chapter 15 – Linear Inequations

**Introduction to Linear inequation**

First of all, we must have an insight over the structure of linear equations which is not expressed in the form of simple expressions. It is found in both one and two variables. When one variable expression is expressed in less than and greater than sign it is called the linear inequation.

**The mathematical expression of Linear inequation **

Let us understand this inequality with an example:

One variable inequation: 2x+3>9

This is one variable based inequation. The solution of this inequation relates to all those values of X which satisfies the equation. This left side is expressed in greater than sign.

The solution to this problem is not difficult to evaluate.

Now, you must consider the example in two variables.

X+2y>5

Here, you can set the value of x and y in such a way that the sum of x and 2y is greater than 5.

Here, you will notice that this is just one of the possible solutions. The whole solution will contain all those values that satisfy the inequation.

These two examples are of strict inequalities. The main existence of this inequality is that the left-hand side and right-hand side of the equation cannot be equal. Leaving such inequalities at one side, there are no further strict guidelines.

The linear inequation contains one variable between two linear expressions. In addition to this, this inequation lies between linear expression and a constant. Many times, some equation contains the one variable only. The linear inequation can be simplified in a general form.

Ax+B>0 or Ax+B>=0

Ax+B<0 or Ax+B<=0

But, this one variable linear inequality does not exceed 0.

### **Discussion of Exercises of RD Sharma Solutions for Class 11 Chapter 15 – Linear Inequations**

- The first exercise has 28 questions. These questions are related to solving basic inequalities of x in relation to R.
- In the second exercise, there are 21 questions. These questions are related to solving the system of equations and they can earn you 3 marks easily in the exam if you have the mastery on them.
- The third exercise again has 28 questions. These questions in the exercise are also based on solving the system of equations, but they are little more complex than the previous exercise as they involve modulus.
- In the fourth exercise, i.e., 15.4, there are 12 questions which are statement based questions.
- In the next exercise, there are 10 questions which are related to the representation of the solutions on graphs.
- There are 16 questions in the sixth exercise of the chapter. These questions are related to the occurrence of no solution in inequality.
- The seventh exercise is dedicated to very short questions. These questions test the base and foundation of your knowledge about inequalities. They are mostly dedicated to finding the value of x.
- At last, there is an exercise which contains 12 MCQs. You have to mark the correct alternative. In these types of questions, hit and trial methods can come to your rescue.

### **Benefits of using RD Sharma Solutions for Class 11 Chapter 15 by instasolv**

Instasolv has created RD Sharma Class 11 Maths Solutions Chapter 15 – Linear Inequation in the simplest subject language so that average students can take a simple understanding of the concept of inequalities. The solutions are free of cost. They include detailed explanations which will help you overcome every difficulty in the learning process. In case of any further doubts in the chapter, you can find instant solutions at our platform.