Class 11 Maths - WEST-BENGAL
Linear Inequalities
The chapter 'Linear Inequalities' in Class 11 Mathematics under the West Bengal Council of Higher Secondary Education (WBCHSE) introduces students to algebraic statements involving 'greater than' or 'less than' symbols rather than strict equality. You will learn to solve linear inequalities in one and two variables algebraically and represent their solutions graphically on a Cartesian plane. This fundamental topic is crucial for scoring well in your Class 11 annual exams and builds a strong foundation for Linear Programming in Class 12, making it a high-scoring and essential chapter for board exam preparation.
Start Learning FreeKey Concepts
Linear Inequality
An algebraic statement involving linear expressions separated by inequality symbols like <, >, ≤, or ≥.
Solution of an Inequality
The value or range of values of the variable that makes the inequality a true statement.
Graphical Representation in Two Variables
Representing the solution region of a linear inequality on a 2D Cartesian plane by shading one side of a boundary line.
Strict vs Slack Inequalities
Strict inequalities use < or > (represented by dashed boundary lines), while slack inequalities use ≤ or ≥ (solid boundary lines).
Important Formulas
Board Exam Info
In the West Bengal (WBCHSE) Class 11 Mathematics examination, this chapter typically carries around 4 to 6 marks. Questions usually include 1-mark multiple-choice questions, 2-mark short answer type problems asking to solve algebraic inequalities, and 4-mark long answer questions requiring graphical solutions of a system of linear inequalities.
Frequently Asked Questions
Why does the inequality sign reverse when multiplying or dividing by a negative number?
Because multiplying or dividing by a negative number reflects numbers across zero on the number line, effectively inverting their relative sizes.
How do I know which side of the line to shade in graphical inequalities?
Choose a test point like (0,0). If substituting it into the inequality makes the statement true, shade the region containing that point; otherwise, shade the opposite side.
When should I use a dashed line instead of a solid line in graphs?
Use a dashed line for strict inequalities (< or >) to show that points on the line are not included in the solution. Use a solid line for ≤ or ≥.
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