Linear Inequalities | Class 11 Mathematics Notes

5.2 Inequalities

This section introduces inequalities through practical examples and formal definitions. Consider Ravi who has ₹200 to buy rice packets priced at ₹30 each. If x is the number of packets, the total cost is 30x. Since he must buy whole packets, he may not spend the entire ₹200, leading to the inequality 30x < 200. This is not an equation because it does not involve equality but a strict inequality. Another example is Reshma who has ₹120 to buy registers and pens costing ₹40 and ₹20 respectively. If x and y are the numbers of registers and pens, the total cost is 40x + 20y ≤ 120. This inequality includes the possibility of spending exactly ₹120 or less. Inequalities can be strict (< or >) or slack (≤ or ≥). They can involve one or two variables. Numerical inequalities compare numbers directly, e.g., 3 < 5, while literal inequalities involve variables, e.g., x < 5. Double inequalities combine two inequalities, such as 3 ≤ x < 5. The section also classifies inequalities into linear inequalities in one variable (ax + b < 0), in two variables (ax + by ≤ c), and quadratic inequalities (ax² + bx + c > 0), though the chapter focuses on linear inequalities only.

🔗 Connection: Prepares for algebraic methods to solve linear inequalities in one variable and their graphical representation in Section 5.3.