NCERT Solutions for Class 11 Mathematics Chapter Linear Inequalities

This worksheet is designed to help Class 11 students understand the concept of linear inequalities in a clear and structured way. Linear inequalities involve comparing algebraic expressions using symbols like <, >, ≤, and ≥. This chapter is important because it helps students solve real-life problems involving limits, constraints, and conditions. This worksheet provides complete and accurate NCERT Solutions that strictly follow the NCERT textbook structure and questions.

Chapter summary: stories, poems & themes

This chapter is fully concept-based and focuses on mathematical understanding rather than stories or poems. It introduces inequalities through real-life situations such as spending money, marks calculation, and measurement constraints. Students learn how to form inequalities, solve them, and represent solutions on a number line. The main theme is logical reasoning and understanding relationships between variables using mathematical expressions.

What this NCERT chapter covers?

• Understanding inequalities and their symbols 
• Difference between equations and inequalities 
• Linear inequalities in one and two variables 
• Rules for solving inequalities 
• Graphical representation on a number line 
• Solving real-life word problems using inequalities

 

How to use these NCERT solutions?

Students should first attempt each question on their own to build problem-solving skills. After solving, they can refer to these NCERT Solutions to verify their answers and understand the correct steps. Parents and teachers can use this worksheet to guide students and explain concepts clearly. The solutions follow the exact NCERT order, making revision simple and effective.

Student tips & learning tricks

• Always check the inequality sign carefully before solving 
• Reverse the inequality sign when multiplying or dividing by a negative number 
• Practice writing solution sets clearly 
• For number line questions, mark open and closed circles correctly 
• Read word problems carefully to form correct inequalities

 

Why NCERT solutions are important?

NCERT Solutions help students learn the correct methods as per CBSE guidelines. They build a strong foundation in mathematics and improve logical thinking. These solutions help students prepare for exams, reduce mistakes, and boost confidence. Regular practice ensures better understanding and accuracy.

Complete answer key – NCERT solutions

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. x < 3 

18. x < 1 

19. x > –5 

20. x ≥ 4 

21. x > –1 

22. x ≥ 82 

23. (5, 7), (7, 9) 

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. –5 < x < 5 

9. –5 < x < 5 

10. –7 ≤ x ≤ 14 

11. 20°C < C < 25°C 

12. 320 < x < 960 

13. 600 < x < 1125 

14. 9.6 ≤ MA ≤ 16.8 

Strengthen your understanding of inequalities with accurate NCERT Solutions for Class 11 Mathematics Chapter Linear Inequalities and improve your problem-solving skills.

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