The solutions for Chapter 15 – Linear Inequations from RD Sharma Class 11 Maths are designed to help students build a strong foundation and perform well in their final exams. This chapter introduces students to the concept of linear inequations involving one and two variables, which play a crucial role in subjects like mathematics, science, engineering, and particularly in linear programming.
Students aiming for high scores can access the RD Sharma Class 11 Maths Solutions in PDF format using the links provided below. These solutions serve as a reliable guide for effective problem-solving and revision.
Chapter 15 includes a total of six exercises, with each question answered in a step-by-step manner. The solutions have been thoughtfully prepared by subject matter experts, following the latest syllabus and exam pattern for 2023–24. The language used is simple and clear, making it easy for students to understand and apply different methods while solving questions efficiently.
RD Sharma Solutions Class 11 Maths Chapter 15 : Overview
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Understanding the concept of an inequation and its solution
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Solving linear inequations in one variable
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Finding the solution set for a system of linear inequations in one variable
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Real-life applications involving linear inequations
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Graphical methods to solve linear inequations in two variables
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Solving pairs of simultaneous linear inequations graphically
RD Sharma Solutions Class 11 Maths Quadratic Equations Question with Answers
Linear Inequations in One Variable
1. Solve: 3x + 5 < 11
Answer: x < 2
2. Solve: 2x − 7 ≥ 1
Answer: x ≥ 4
3. Solve: 5 − 2x ≤ 1
Answer: x ≥ 2
4. Solve: 3x − 2 > 4x + 1
Answer: x < −3
5. Solve: −4x + 3 < 7x − 8
Answer: x > 1
6. Solve: 7 − x ≥ 2x + 1
Answer: x ≤ 2
7. Solve: 2(x + 3) > x − 4
Answer: x > −10
8. Solve: −3(x − 5) ≤ 2(x + 1)
Answer: x ≥ 13/5
9. Solve: x/3 − 2 ≥ 1
Answer: x ≥ 9
10. Solve: −x/4 < 2
Answer: x > −8
Solution Set on a Number Line
11. Solve and graph: x − 4 ≤ 2
Answer: x ≤ 6
12. Solve and graph: 2x + 1 > −3
Answer: x > −2
Word Problems
13. A number exceeds 5 but is less than 9.
Answer: 5 < x < 9
14. The cost of a pen is at least ₹15 and at most ₹25.
Answer: 15 ≤ x ≤ 25
15. The speed of a train should not exceed 80 km/h.
Answer: x ≤ 80
System of Inequations (One Variable)
16. Solve: x > 2 and x < 7
Answer: 2 < x < 7
17. Solve: x ≤ 3 and x ≥ −2
Answer: −2 ≤ x ≤ 3
18. Solve: 2x + 3 > 5 and x − 1 < 4
Answer: 1 < x < 5
19. Solve: 4x − 1 ≥ 7 and 2x + 5 ≤ 13
Answer: 2 ≤ x ≤ 4
20. Solve: x − 2 ≤ 1 and x + 3 ≥ 0
Answer: −3 ≤ x ≤ 3
Inequations with Rational Expressions
21. Solve: (x − 1)/(x + 2) < 0
Answer: x ∈ (−2, 1)
22. Solve: (2x − 3)/(x + 1) ≥ 0
Answer: x ∈ (−∞, −1) ∪ [3/2, ∞)
23. Solve: (x² − 9)/(x − 2) > 0
Answer: x ∈ (−∞, −3) ∪ (2, 3) ∪ (3, ∞)
24. Solve: 1/(x − 3) < 0
Answer: x < 3
Graphical Solutions in Two Variables
25. Solve graphically: x + y ≤ 6
Answer: Shade region below line x + y = 6 (inclusive)
26. Solve graphically: 2x + 3y > 12
Answer: Shade region above 2x + 3y = 12, dashed line
27. Solve graphically: y ≥ 2x − 1
Answer: Shade region above the line including it
28. Solve graphically: x ≥ 0, y ≥ 0, x + y ≤ 5
Answer: Region in first quadrant bounded by x + y = 5
Application-Based Problems
29. Study time between 5 and 10 hours
Answer: 5 ≤ x ≤ 10
30. Production between 50 and 100 units
Answer: 50 ≤ x ≤ 100
31. Solve: 3x + 4 < 2x + 7 and x ≥ 0
Answer: 0 ≤ x < 3
32. Solve: x² < 4
Answer: −2 < x < 2
33. Solve: |x − 2| < 3
Answer: −1 < x < 5
34. Solve: |x + 1| ≥ 4
Answer: x ≤ −5 or x ≥ 3
35. Solve: x − 2 ≥ 3 or 2x + 1 < 5
Answer: x ≥ 5 or x < 2
Frequently Asked Questions
Chapter 15 – Linear Inequations contains six exercises. Each exercise is designed to progressively enhance students' understanding, from basic linear inequalities to complex graphical solutions involving two variables. These exercises also include practical and real-life applications of inequalities.
Linear inequations form the basis of many real-world applications, such as business constraints, science models, and engineering design. Understanding how to solve and interpret inequalities helps students develop logical reasoning and problem-solving skills. It's also essential for competitive exams like JEE, NDA, and various Olympiads.
You can download RD Sharma Solutions for Class 11 Chapter 15 – Linear Inequations in PDF format from trusted educational platforms like Infinity Learn, where solutions are provided exercise-wise with step-by-step explanations, based on the 2025–26 syllabus.
Yes, absolutely. The RD Sharma solutions provide a comprehensive understanding of each concept, including detailed steps for each question. The solutions are prepared by subject experts, ensuring clarity and accuracy. Practicing these can significantly improve your exam performance and confidence.
Linear equations use equal signs (=), while linear inequations involve inequality symbols such as <, ≤, >, or ≥. While linear equations have a single definite solution, inequations have a range or set of solutions depending on the inequality involved.