RD Sharma Solutions for Class 11 Maths Chapter 15 - Free PDF Download
FAQs on RD Sharma Class 11 Maths Solutions Chapter 15 - Linear Inequations
1. Where can I find reliable, step-by-step RD Sharma Solutions for Class 11 Maths Chapter 15, Linear Inequations?
You can find comprehensive and expert-verified RD Sharma Solutions for Class 11 Maths Chapter 15 on Vedantu. Our solutions are crafted to provide clear, step-by-step guidance for every problem in the textbook, ensuring you understand the correct methodology for solving linear inequations. These are available online to help you with your homework and exam preparation for the 2025-26 academic session.
2. How do Vedantu's RD Sharma solutions for Class 11 Maths Chapter 15 help in scoring better marks?
Vedantu's solutions are designed by subject matter experts to build a strong conceptual foundation. By using our solutions for Chapter 15, you can:
- Understand the step-by-step logic for solving different types of linear inequations.
- Learn to correctly apply the rules of inequalities, especially when dealing with negative numbers.
- Gain proficiency in both algebraic and graphical methods of solving problems, as per the CBSE syllabus.
- Practise a wide variety of questions, which improves speed and accuracy in exams.
3. What is the correct method for solving one-variable linear inequations as per the RD Sharma textbook?
The standard method involves a few key steps:
- Step 1: Simplify both the Left-Hand Side (LHS) and Right-Hand Side (RHS) of the inequation by removing brackets and combining like terms.
- Step 2: Transpose variable terms to one side and constant terms to the other, just as you would with a linear equation.
- Step 3: Isolate the variable. This is the critical step where you must remember to reverse the inequality symbol if you multiply or divide both sides by a negative number.
- Step 4: Represent the solution set on a number line, using a hollow circle for strict inequalities (<, >) and a solid dot for slack inequalities (≤, ≥).
4. How do the solutions explain the graphical method for solving linear inequalities in two variables found in Chapter 15?
The solutions explain the graphical method clearly by breaking it down into a systematic process:
1. First, treat the inequation as an equation to determine the boundary line.
2. Next, determine if this line should be solid (for ≤ or ≥) or dotted (for < or >).
3. Then, select a test point (usually (0,0) if it's not on the line) and substitute it into the original inequation.
4. If the test point satisfies the inequation, you shade the entire region containing that point. If it doesn't, you shade the opposite region. This shaded area is the graphical solution.
5. What is the most common mistake students make when solving problems in RD Sharma Chapter 15, and how can it be avoided?
The most frequent and critical mistake is forgetting to reverse the inequality symbol when multiplying or dividing both sides of an inequation by a negative number. For instance, in -2x > 6, dividing by -2 changes the inequation to x < -3. To avoid this error, always pause and check the sign of the number you are multiplying or dividing by. If it is negative, make it a habit to immediately flip the inequality sign.
6. How does the solution to a linear inequation differ from the solution to a linear equation?
The primary difference lies in the nature of the solution. A linear equation, such as ax + b = c, typically yields a single, unique value for the variable. In contrast, a linear inequation, like ax + b > c, results in a range of infinite solutions, which is represented as an interval or a region. For example, the solution to x = 5 is just the number 5, while the solution to x > 5 includes every number greater than 5.
7. In the graphical solutions for Chapter 15, what is the significance of using a dotted line versus a solid line?
The type of line used indicates whether the points on the boundary are part of the solution.
- A dotted line is used for strict inequalities (< or >). It signifies that the points lying on the line are not included in the solution set.
- A solid line is used for slack or non-strict inequalities (≤ or ≥). It signifies that the points on the line are included in the solution set.
8. Why is it necessary to solve a system of linear inequalities, and what does the final shaded solution region represent?
Solving a system of linear inequalities is necessary when a problem has multiple conditions or constraints that must all be satisfied simultaneously. For example, in a business problem, you might have constraints on both production time and material costs. The final overlapping shaded area, known as the 'feasible region', represents the set of all possible solutions (x, y) that satisfy every single inequation in the system.
9. What is the difference between a 'strict' inequality and a 'slack' inequality when representing the solution on a number line?
The difference relates to whether the endpoint is included in the solution set. A 'strict' inequality (like x > 3 or x < 3) excludes the endpoint. On a number line, this is represented with an open or hollow circle at the number 3. A 'slack' inequality (like x ≥ 3 or x ≤ 3) includes the endpoint. This is represented with a closed or solid dot at the number 3, indicating that 3 itself is a valid solution.
