Linear Inequalities | Class 11 Mathematics Notes

5.1 Introduction

In earlier classes, students have studied equations involving one or two variables and solved problems by translating statements into equations. However, not all real-world problems can be expressed as equations. Some statements involve comparisons rather than equalities, such as 'less than', 'greater than', 'less than or equal to', or 'greater than or equal to'. These comparisons are represented by inequalities using the symbols <, >, ≤, and ≥. For example, the height of all students in a class might be less than 160 cm, or a classroom might accommodate at most 60 tables or chairs. These statements cannot be represented by equations but by inequalities. This chapter introduces linear inequalities in one and two variables, which are fundamental in various fields such as science, mathematics, statistics, economics, and psychology. Understanding inequalities helps in solving practical problems where quantities are bounded or constrained but not necessarily equal.

🔗 Connection: Leads to the formal introduction and definition of inequalities with practical examples in Section 5.2.