Class 11 Maths - HARYANA
Linear Inequalities
The chapter 'Linear Inequalities' in Class 11 Mathematics builds upon your knowledge of linear equations by introducing inequalities involving symbols like <, >, ≤, and ≥. This chapter covers algebraic solutions of linear inequalities in one and two variables, and their graphical representations. For Haryana (BSEH) board exams, this is a scoring topic that lays the foundation for Linear Programming in Class 12. Mastering this chapter helps you solve optimization problems and understand constraint-based mathematics used in economics, science, and engineering.
Start Learning FreeKey Concepts
Linear Inequality in One Variable
An inequality that contains a linear expression in one variable, such as ax + b < 0, where a ≠ 0.
Linear Inequality in Two Variables
An inequality involving two variables, such as ax + by < c, which represents a half-plane on the Cartesian coordinate system.
Solution of an Inequality
A value or a set of values of the variable(s) that makes the inequality a true statement.
Graphical Representation
The method of plotting the boundary line on a graph and shading the region that satisfies the given inequality.
System of Linear Inequalities
A set of two or more linear inequalities considered simultaneously, whose common solution region represents the feasible region.
Important Formulas
Board Exam Info
In the Haryana (BSEH) Class 11 Mathematics exam, Linear Inequalities typically carries around 4 to 6 marks. Common question types include solving algebraic inequalities in one variable and showing the solution set on a number line, as well as solving systems of linear inequalities graphically in two variables.
Frequently Asked Questions
When do we reverse the inequality sign?
We reverse the inequality sign (e.g., from < to >) whenever we multiply or divide both sides of the inequality by a negative number.
How do we know which side of the line to shade in graphical inequalities?
Choose a test point (like origin (0,0) if it doesn't lie on the line). Substitute its coordinates into the inequality; if it makes the statement true, shade the side containing the point. Otherwise, shade the opposite side.
What is the difference between strict and slack inequalities?
Strict inequalities use < or > and do not include the boundary points (represented by a dashed line). Slack inequalities use ≤ or ≥ and include the boundary points (represented by a solid line).
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