Class 11 Maths - KARNATAKA
Linear Inequalities
The chapter 'Linear Inequalities' in Class 11 Mathematics builds upon your knowledge of linear equations by introducing inequality symbols like <, >, ≤, and ≥. You will learn to solve linear inequalities in one and two variables algebraically and represent their solutions graphically on a number plane. This chapter is fundamental for understanding linear programming in Class 12 and carries significant weight in Karnataka (KSEEB) board exams. Mastering graphical solutions and algebraic manipulation of inequalities will help you score high marks in both short-answer and long-answer exam sections.
Start Learning FreeKey Concepts
Inequality
A mathematical statement involving an inequality symbol (like <, >, ≤, or ≥) comparing two expressions.
Linear Inequality in One Variable
An inequality of the form ax + b < 0 (or ≤, >, ≥) where a ≠ 0, having a single variable x.
Linear Inequality in Two Variables
An inequality involving two variables, such as ax + by < c, whose solution region is a half-plane in a Cartesian coordinate system.
Rules for Solving Algebraic Inequalities
Equal numbers can be added/subtracted, and positive numbers can multiply/divide both sides without reversing the inequality sign, but multiplying or dividing by a negative number reverses the inequality symbol.
Graphical Solution of Linear Inequalities
The process of plotting the boundary line on a graph and shading the correct half-plane region that satisfies the given inequality.
Important Formulas
Board Exam Info
In the Karnataka (KSEEB) Class 11 Mathematics board exams, this chapter typically carries around 5 to 8 marks. Questions usually include 1-mark or 2-mark algebraic inequality solving problems, and a 3-mark or 5-mark graphical question on solving a system of linear inequalities in two variables.
Frequently Asked Questions
When do we reverse the inequality sign?
You must reverse the inequality sign (e.g., change < to >) whenever you multiply or divide both sides of the inequality by a negative number.
How do I know which side of the line to shade in a graphical inequality?
Choose a test point (like origin (0,0)) not on the boundary line. Substitute it into the inequality; if the statement is true, shade the side containing the point. If false, shade the opposite side.
What is the difference between strict and slack inequalities?
Strict inequalities use < or > and are represented by dotted boundary lines on graphs. Slack inequalities use ≤ or ≥ and are represented by solid boundary lines.
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