Class 11 Maths - RAJASTHAN
Linear Inequalities
The chapter 'Linear Inequalities' in Class 11 Mathematics introduces students to algebraic inequalities involving one or two variables. Building upon linear equations, this chapter teaches how to represent conditions using symbols like <, >, ≤, and ≥. Students will learn to solve inequalities in a single variable algebraically and represent their solutions on a number line. Additionally, the chapter covers graphical solutions of linear inequalities in two variables and systems of inequalities, which form the foundational basis for Linear Programming in Class 12. Mastering this chapter is crucial for scoring well in Rajasthan (RBSE) board examinations.
Start Learning FreeKey Concepts
Inequality
A mathematical statement comparing two expressions using inequality symbols such as <, >, ≤, or ≥.
Linear Inequality in One Variable
An inequality of the form ax + b < 0 (or ≤, >, ≥) where a ≠ 0, having a range of real numbers as its solution.
Linear Inequality in Two Variables
An inequality involving two variables, like ax + by < c, whose solution region is represented by a half-plane on the Cartesian coordinate system.
Graphical Solution
The method of representing the solution set of linear inequalities in two variables on a graph using a shaded half-plane.
Strict vs Slack Inequalities
Strict inequalities use < or > (represented by a dashed line on graphs), while slack inequalities use ≤ or ≥ (represented by a solid line).
Important Formulas
Board Exam Info
In the Rajasthan (RBSE) Class 11 Mathematics board examinations, this chapter typically carries around 4 to 6 marks. Common question types include solving algebraic inequalities in one variable and showing the solution on a number line, as well as finding the graphical solution region for a system of linear inequalities in two variables.
Frequently Asked Questions
Why does the inequality sign reverse when multiplying or dividing by a negative number?
Because multiplying or dividing both sides of an inequality by a negative number flips the orientation of numbers on the number line, reversing the comparison.
How do I know whether to use a solid line or a dashed line when graphing inequalities?
Use a solid line for '≤' or '≥' because the boundary points are included in the solution. Use a dashed line for '<' or '>' because the boundary points are not included.
How do I determine which side of the line to shade in a graph?
Substitute a test point, usually the origin (0, 0), into the inequality. If the statement is true, shade the side containing the origin; if false, shade the opposite side.
Learn Linear Inequalities with Your AI Tutor
10 different ways to study this chapter. Free for 3 chapters per day.
Lecture
Key Points
Interactive
Quiz
Flashcards