Class 11 Maths - MAHARASHTRA
Linear Inequalities
The chapter 'Linear Inequalities' in Class 11 Mathematics introduces students to algebraic inequalities involving one or two variables. Building upon linear equations from earlier classes, this chapter explores how to represent constraints graphically in a Cartesian plane and solve systems of simultaneous linear inequalities. Mastery of this topic is crucial as it lays the foundation for Linear Programming, a high-weightage topic in Class 12. For MSBSHSE board exams, students frequently encounter questions involving graphical solutions and word problems, making it a scoring chapter that requires clear conceptual understanding and precision in plotting graphs.
Start Learning FreeKey Concepts
Algebraic Inequality
A statement involving variables and inequality symbols like <, >, ≤, or ≥ which indicates that one expression is strictly less than, greater than, or equal to another.
Linear Inequality in One Variable
An inequality of the form ax + b < 0 (or ≤, >, ≥) where a ≠ 0, having a solution set represented on a number line.
Linear Inequality in Two Variables
An expression of the form ax + by < c (or ≤, >, ≥) whose solutions are represented by a half-plane on the Cartesian coordinate system.
Solution Region (Feasible Region)
The common region shared by the graphs of a system of linear inequalities that satisfies all the given constraints simultaneously.
Strict vs Slack Inequalities
Strict inequalities use < or > and are represented by dashed boundary lines, while slack inequalities use ≤ or ≥ and use solid boundary lines.
Important Formulas
Board Exam Info
In the Maharashtra State Board (MSBSHSE) Class 11 Mathematics examinations, the chapter on Linear Inequalities typically carries around 4 to 6 marks. Common question types include solving linear inequalities in one variable algebraically, solving a system of linear inequalities in two variables graphically, and determining the feasible region for a set of given constraints.
Frequently Asked Questions
How do I know which side of the line to shade in a two-variable inequality?
Choose a test point, usually the origin (0,0), and substitute it into the inequality. If the resulting statement is true, shade the side containing the test point; if false, shade the opposite side.
When should I use a dashed line instead of a solid line?
Use a dashed line for strict inequalities (< or >) to show that points on the line are not part of the solution. Use a solid line for slack inequalities (≤ or ≥) to indicate the boundary line is included.
Can I multiply or divide both sides of an inequality by a negative number?
Yes, but you must reverse the inequality symbol (e.g., changing < to > or ≤ to ≥) whenever you multiply or divide by a negative number.
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