Linear Inequalities | Class 11 Mathematics Notes

5.3 Algebraic Solutions of Linear Inequalities in One Variable and their Graphical Representation

This section explains how to solve linear inequalities in one variable algebraically and represent their solutions graphically. Using the example 30x < 200, where x is the number of rice packets, the solution involves finding values of x that satisfy the inequality. By testing integer values, it is found that x = 0,1,2,3,4,5,6 satisfy 30x < 200, while x = 7 does not. These values form the solution set. However, trial and error is inefficient, so algebraic rules are introduced. The key rules for solving inequalities are: (1) Adding or subtracting the same number on both sides does not change the inequality; (2) Multiplying or dividing both sides by a positive number keeps the inequality sign unchanged; (3) Multiplying or dividing both sides by a negative number reverses the inequality sign. Several examples illustrate these rules, including solving inequalities for natural numbers, integers, and real numbers. Graphical representation on the number line is also shown, where open circles represent strict inequalities and closed circles represent inclusive inequalities. This section establishes the foundation for solving and visualizing linear inequalities in one variable.

📊 Diagram: Fig 5.1; Fig 5.2

🔗 Connection: Leads to worked examples and exercises to practice solving linear inequalities and graphing solutions.