Class 11 Maths - ODISHA
Linear Inequalities
The chapter 'Linear Inequalities' in Class 11 Mathematics for Odisha (BSE) students extends the study of equations to inequalities involving two variables. You will learn how to solve algebraic linear inequalities in one and two variables and represent their solutions graphically on a Cartesian plane. This topic is fundamental for linear programming problems in higher classes and regularly features in board examinations. Mastering this chapter helps build strong analytical and graphical problem-solving skills, which are crucial for scoring high marks in mathematics.
Start Learning FreeKey Concepts
Linear Inequality
A statement involving variables and the inequality symbols (<, >, ≤, ≥) where the highest power of variables is 1.
Solution of an Inequality
The set of all values of the variable that makes the inequality a true statement.
Graphical Representation
Representing the solution region of a linear inequality in two variables on a Cartesian plane using shaded regions and solid or dashed lines.
Strict vs Slack Inequalities
Strict inequalities use < or > (represented by dashed boundary lines), while slack inequalities use ≤ or ≥ (represented by solid boundary lines).
Rules for Solving
Equal numbers can be added or subtracted, and both sides can be multiplied or divided by positive numbers without reversing the inequality sign; however, multiplying or dividing by a negative number reverses the sign.
Important Formulas
Board Exam Info
In the Odisha (BSE) Class 11 Mathematics examinations, this chapter typically carries around 4 to 6 marks. Common question types include solving linear inequalities algebraically in one variable, showing the solution on a number line, and solving a system of linear inequalities graphically in two variables.
Frequently Asked Questions
When do we reverse the inequality sign?
You must reverse the inequality sign (from < to >, or ≥ to ≤) whenever you multiply or divide both sides of the inequality by a negative number.
What is the difference between a solid line and a dashed line in graphical solutions?
A solid line is used for '≤' or '≥' indicating that the points on the line are included in the solution. A dashed line is used for '<' or '>' indicating that the points on the line are not included.
How do we find the correct half-plane to shade?
Choose a test point (usually the origin (0,0) if it does not lie on the line) and substitute its coordinates into the inequality. If it satisfies the inequality, shade the region containing that point; otherwise, shade the opposite region.
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