← GSEB Class 11
Linear Inequalities
Chapter Overview
Linear inequalities use symbols <, <=, >, >=. Solving follows equation rules except multiplying/dividing by a negative reverses the inequality sign. The chapter covers solving in one variable, number line representation, and graphical solutions in two variables using half-planes.
Topics Covered
- Properties of Inequalities
- Solving in One Variable
- Number Line Representation
- Solving in Two Variables
- Graphical Method
- Half-Planes
- Systems of Inequalities
Key Formulas
If a > b and c > 0, then ac > bc
If a > b and c < 0, then ac < bc
Ax + By <= C represents a half-plane
Real-World Applications
Applications: Linear programming, economics, resource constraints, and optimization problems.
Study Tips
Tip: Remember sign reversal when multiplying by negatives
Tip: Draw graphs carefully for two-variable problems
Tip: Test points to determine solution region