NCERT solutions for Class 11 Mathematics Chapter Linear inequalities – complete answers & explanations

Linear inequalities is an important chapter in Class 11 Mathematics that introduces students to solving mathematical statements involving inequality signs like less than, greater than, and their combinations. This chapter helps learners understand how quantities can be compared rather than equated, which is useful in real-life situations like budgeting, measurements, and constraints. It builds a strong foundation for algebra and higher-level mathematics. With clear and reliable NCERT solutions, students can learn the correct approach to solving different types of inequalities. Download the worksheet and practice alongside solutions for better clarity. This will help students identify patterns and avoid mistakes. Regular practice also improves speed and accuracy in exams. Book a free trial now to get expert guidance and strengthen understanding of important concepts.

What this NCERT chapter covers?

1. Understanding the concept of inequalities and how they differ from equations 
2. Use of inequality symbols like <, >, ≤, and ≥ in mathematical expressions 
3. Solving linear inequalities in one variable using algebraic methods 
4. Learning rules for adding, subtracting, multiplying, and dividing inequalities 
5. Understanding how inequality signs change when multiplied or divided by negative numbers 
6. Representing solutions of inequalities on a number line 
7. Solving word problems involving real-life situations using inequalities 
8. Finding solution sets in natural numbers, integers, and real numbers 
9. Working with double inequalities and compound inequalities 
10. Applying inequalities to practical problems like marks, temperature, and measurements 
11. Developing logical reasoning and analytical thinking skills 
12. Preparing for exam-based questions through structured problem-solving 

How to use these NCERT solutions?

1. Start by reading each question carefully from the worksheet before looking at the solution 
2. Try solving the question on your own to build confidence and understanding 
3. Use the provided answers to check your approach and final answer 
4. Focus on understanding the steps used rather than memorising answers 
5. Practice questions multiple times to improve speed and accuracy 
6. Follow the exact order of questions as given to maintain consistency 
7. Parents and teachers can guide students by discussing mistakes and clarifying doubts 
8. Revise difficult questions regularly to strengthen concepts 
9. Use number line representation wherever required for better clarity 
10. Ensure all steps are written neatly as expected in exams 

Important tips & tricks for students

1. Always pay attention to the direction of the inequality sign while solving 
2. Remember to reverse the inequality sign when multiplying or dividing by a negative number 
3. Avoid skipping steps while solving algebraic inequalities 
4. Practice number line representation regularly for better visualization 
5. Carefully read word problems to identify the correct inequality 
6. Write answers in proper mathematical form such as intervals or inequalities 
7. Double-check calculations to avoid small errors 
8. Understand the concept instead of memorising patterns 
9. Practice both simple and complex inequalities to gain confidence 
10. Focus on clarity and neat presentation to score full marks 

NCERT solutions – complete answer key

EXERCISE 5.1

1. 
(i) 1, 2, 3, 4 
(ii) …, –4, –3, –2, –1, 0, 1, 2, 3, 4 

2. 
(i) No solution 
(ii) …, –3, –2, –1 

3. 
(i) …, –1, 0, 1 
(ii) x < 2 

4. 
(i) …, –2, –1, 0 
(ii) x > –2 

5. x > –4 
6. x < –3 
7. x ≤ –5 
8. x ≤ 4 
9. x < 2 
10. x > 1 
11. x ≤ 4 
12. x ≥ –6 
13. x < –1 

14. x < 4 
15. x ≥ 3 
16. x ≥ 35 
17. (5, 7), (7, 9) 
18. x < 3 
19. x < 1 
20. x > –5 
21. x ≥ 4 
22. x > –1 
23. x ≥ 82 

24. (6, 8), (8, 10) 
25. Shortest side ≥ 9 cm 
26. x ≥ 8 and x ≤ 22 

MISCELLANEOUS EXERCISE

1. 2 ≤ x ≤ 3 
2. –6 ≤ x ≤ 4 
3. –5 < x ≤ 5 
4. –2 ≤ x < 1 
5. –11 ≤ x ≤ 11 
6. –10 < x ≤ 2 
7. –1 < x < 3 
8. 
9. 
10. 

11. –5 < x < 5 
12. –5 < x < 5 
13. –7 ≤ x ≤ 14 
14. 20°C < C < 25°C 
15. 320 < x < 960 
16. 600 < x < 1125 
17. 9.6 ≤ MA ≤ 16.8 

Why NCERT solutions help students?

NCERT solutions help students prepare effectively for exams by providing clear and accurate answers aligned with the expected format. They improve concept clarity, help in understanding the correct solving approach, and build confidence while attempting different types of questions. Regular practice with these solutions ensures better performance and reduces exam stress.

Help your child build strong Mathematics fundamentals with expert-guided learning support.
Book a free trial!