Class 11 Maths - MP
Linear Inequalities
The Chapter 'Linear Inequalities' in Class 11 Mathematics under the Madhya Pradesh Board (MPBSE) introduces students to algebraic expressions involving inequality symbols like <, >, <=, and >=. Students will learn how to solve linear inequalities in one and two variables algebraically and represent their solutions graphically on a number line or coordinate plane. This chapter builds a strong foundation for Linear Programming in Class 12 and carries significant weight in board exams, frequently appearing in short-answer and long-answer question formats.
Start Learning FreeKey Concepts
Inequality
A statement involving an inequality symbol comparing two real numbers or algebraic expressions.
Linear Inequality in One Variable
An inequality of the form ax + b < 0 (or <=, >, >=) where a != 0, containing a single variable x.
Linear Inequality in Two Variables
An inequality involving two variables, such as ax + by < c, whose solution region is a half-plane in the Cartesian coordinate system.
Graphical Solution
Representing the solution set of a linear inequality in two variables on a graph using shaded regions and solid or dashed boundary lines.
Rules for Solving Inequalities
Operations like adding, subtracting, or multiplying/dividing by positive numbers preserve the inequality sign, while multiplying or dividing by a negative number reverses the inequality sign.
Important Formulas
Board Exam Info
In the Madhya Pradesh (MPBSE) Class 11 Mathematics examination, this chapter typically carries around 4 to 6 marks. Common question types include solving linear inequalities in one variable algebraically and representing the solution on a number line, as well as solving systems of linear inequalities in two variables graphically.
Frequently Asked Questions
When does the inequality sign reverse?
The inequality sign reverses when 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 inequalities involving <= or >= (inclusive), indicating that points on the line are included in the solution. A dashed line is used for < or > (strict), indicating points on the line are not included.
How do we find the test point for shading a graph?
You can choose any point not on the boundary line (most easily (0,0)) and substitute its coordinates into the inequality. If it makes the statement true, shade the region containing that point; if false, shade the opposite region.
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