Class 11 Maths - BIHAR
Linear Inequalities
The chapter Linear Inequalities in Class 11 Mathematics introduces students to algebraic expressions involving inequality symbols like <, >, ≤, and ≥. Building upon linear equations, this chapter covers the solution of linear inequalities in one and two variables, and their graphical representations on a number plane. For Bihar Board (BSEB) students, mastering this chapter is essential as it forms the foundational base for linear programming and optimization problems in higher classes. Board exams frequently test conceptual clarity through short answer questions requiring graphical solutions and algebraic manipulations of inequalities.
Start Learning FreeKey Concepts
Inequality
A statement involving variables and the symbols <, >, ≤, or ≥ which shows that one quantity is strictly greater or less than, or less than or equal to, another.
Linear Inequality in One Variable
An inequality of the form ax + b < 0 (or with other inequality symbols) where a ≠ 0, solved by applying standard algebraic operations without reversing the inequality sign except when multiplying or dividing by a negative number.
Linear Inequality in Two Variables
An inequality of the form ax + by < c, whose solutions are represented graphically by a half-plane on the Cartesian coordinate system separated by a boundary line.
Graphical Solution
The method of plotting the boundary line as a solid line (for ≤ or ≥) or dashed line (< or >) and shading the region that satisfies the given inequality.
System of Linear Inequalities
A set of two or more linear inequalities considered simultaneously, where the solution is the common overlapping region of all individual inequalities.
Important Formulas
Board Exam Info
In the Bihar (BSEB) Class 11 Mathematics examinations, Linear Inequalities typically carries around 4 to 6 marks. Questions usually include 1 objective (MCQ) question and 1 short-answer or long-answer question based on solving a system of linear inequalities graphically.
Frequently Asked Questions
When do we reverse the inequality sign?
We reverse the inequality sign (e.g., changing < to >) whenever we 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 when the inequality includes 'less than or equal to' (≤) or 'greater than or equal to' (≥), indicating that points on the line are included in the solution. A dashed line is used for strict inequalities (< or >), indicating points on the line are not included.
How do we find the correct half-plane to shade?
Choose a test point (most commonly the origin (0,0)) that does not lie on the boundary line. Substitute its coordinates into the inequality; if the statement is true, shade the side containing the test point. If false, shade the opposite side.
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