Class 11 Maths - TAMILNADU
Linear Inequalities
The Chapter Linear Inequalities in Class 11 Mathematics under the Tamil Nadu Samacheer Kalvi syllabus introduces students to algebraic expressions involving inequality symbols like less than, greater than, or equal to. This chapter builds upon linear equations by extending them to regions on a number line and the Cartesian plane. Students will learn to solve system of linear inequalities in one and two variables and represent their solutions graphically. This topic is fundamental for linear programming problems in higher classes and carries significant weight in board examinations, testing both analytical and graphical skills.
Start Learning FreeKey Concepts
Algebraic Inequality
A statement involving variables and real numbers connected by inequality symbols such as <, >, ≤, or ≥.
Solution of an Inequality
The set of all real numbers or ordered pairs that make the given inequality a true statement.
Graphical Solution in Two Variables
The region in the Cartesian plane bounded by a line that satisfies the given linear inequality.
Half-Plane
A straight line divides the Cartesian plane into two parts, each called a half-plane, where one represents the solution region.
Important Formulas
Board Exam Info
In the Tamil Nadu Samacheer Kalvi Class 11 Mathematics board examination, Linear Inequalities typically carries around 5 to 8 marks. Questions generally include 1-mark objective questions, 2-mark or 3-mark short answer problems involving solving inequalities in one variable, and 5-mark long answer questions requiring graphical representation of a system of linear inequalities in two variables.
Frequently Asked Questions
When do we reverse the inequality sign?
We reverse the inequality sign when we multiply or divide both sides of an inequality by a negative number.
How do we know which side of the line to shade in a graph?
We use a test point, usually the origin (0,0). If the test point satisfies the inequality, we shade the region containing that point; otherwise, we shade the opposite side.
What is the difference between strict and slack inequalities?
Strict inequalities use < or > and are represented by dashed lines on a graph, while slack inequalities use ≤ or ≥ and are represented by solid lines.
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