Class 11 RS Aggarwal Chapter-6 Linear Inequations (In one variable) Solutions - Free PDF Download
FAQs on RS Aggarwal Class 11 Solutions Chapter-6 Linear Inequations (In one variable)
1. What types of problems are covered in the RS Aggarwal Class 11 Solutions for Chapter 6, Linear Inequations?
The solutions for this chapter primarily focus on solving linear inequations in one variable. This includes finding solution sets for different domains like integers, natural numbers, and real numbers. A key part of the solutions is demonstrating how to represent these solution sets on a number line. The chapter also includes solutions for word problems, which first need to be translated into a mathematical inequation.
2. What is the correct first step when solving a linear inequation from RS Aggarwal Chapter 6?
The correct first step is to simplify the inequation by gathering all terms with the variable (e.g., 'x') on one side and all constant terms on the other. This is achieved by adding or subtracting the same value from both sides of the inequation. The primary goal is to isolate the variable and express the inequation in a simple form like ax > b or ax ≤ c, which makes finding the solution set straightforward.
3. How do you represent the solution of an inequation like 'x < 5' on a number line as per the CBSE curriculum?
To represent 'x < 5' on a number line for real numbers, you must follow these steps:
Locate the number 5 on the number line.
Place an open circle (a hollow dot) at 5. This signifies that the value 5 is not included in the solution set.
Draw a thick line or arrow extending from the open circle to the left, towards negative infinity, to cover all numbers less than 5.
For an inequation like 'x ≤ 5', a closed circle (a filled dot) would be used to show that 5 is included.
4. Under what condition must you reverse the inequality symbol when solving an inequation?
You must reverse the inequality symbol (e.g., changing '>' to '<') whenever you multiply or divide both sides of the inequation by a negative number. For example, to solve -3x > 12, you would divide both sides by -3. In doing so, you must reverse the '>' to '<', giving the correct solution x < -4. This is one of the most critical rules in solving inequalities and a common point of error for students.
5. What is the fundamental difference between the solution of a linear equation and a linear inequation?
The fundamental difference is in the nature of the solution. A linear equation, such as 5x - 10 = 0, typically yields a single, discrete value for the variable (here, x = 2). In contrast, a linear inequation, like 5x - 10 > 0, yields a range of values or an interval that satisfies the condition (here, x > 2). The solution to an inequation is a set of infinite numbers, not just one.
6. Why is the solution to a linear inequation in one variable represented as an interval on the number line?
An inequation defines a condition of being 'greater than' or 'less than' a certain value, not 'equal to' it. This condition is not met by a single point but by a continuous range of numbers. For example, the inequation x > 4 is a true statement for 4.1, 5, 100, and all other numbers to the right of 4 on the number line. An interval is used to visually and mathematically represent this entire set of infinite solutions that satisfy the inequation.
7. Are there multiple correct methods to solve a single linear inequation in this chapter?
Yes, it is possible to use different sequences of valid algebraic steps to arrive at the correct solution. As long as the fundamental rules of inequalities are consistently applied, the final solution set will be the same. For instance, you can choose to move variables to the left-hand side or the right-hand side. Both paths are correct if they respect the rules, especially the one about reversing the inequality sign when dealing with negative multipliers or divisors.
8. How are the exercises structured in RS Aggarwal Class 11 Maths Chapter 6?
Chapter 6 on Linear Inequations in one variable is structured with two primary exercises to ensure comprehensive practice, as per the 2025-26 syllabus. The structure is as follows:
Exercise 6A: This is a large exercise with approximately 46 questions covering various types of inequations and their solutions for different domains (integers, real numbers).
Exercise 6B: This exercise is shorter, with about 12 questions, and includes problems that often require multi-step solutions, reinforcing the concepts from the first exercise.
