Class 11 Maths - GUJARAT
Linear Inequalities
The Chapter 'Linear Inequalities' in Class 11 Mathematics under the Gujarat Secondary and Higher Secondary Education Board (GSEB) introduces students to algebraic expressions involving inequality symbols like <, >, ≤, and ≥. This chapter builds upon linear equations by exploring ranges of solutions rather than single fixed values. Students learn to solve linear inequalities in one and two variables algebraically and graphically, representing solutions on a number line or coordinate plane. This fundamental topic is crucial for scoring high in board exams and forms the bedrock for advanced mathematical concepts like Linear Programming in Class 12.
Start Learning FreeKey Concepts
Linear Inequality
An algebraic statement involving a linear expression and an inequality symbol where the highest power of the variable is 1.
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 an inequality in a Cartesian plane, bounded by a line which is solid for '≤' or '≥' and dashed for '<' or '>'.
Rules for Solving Inequalities
Operations like adding, subtracting, multiplying, or dividing positive numbers keep the inequality sign unchanged, but multiplying or dividing by a negative number reverses the sign.
Important Formulas
Board Exam Info
In the Gujarat (GSEB) Class 11 Mathematics board exams, this chapter typically carries around 4 to 6 marks. Common question types include solving algebraic linear inequalities in one variable and showing the solution on a number line, as well as solving systems of linear inequalities in two variables graphically.
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 the numbers across zero on the number line, flipping their relative order of magnitude.
When should I use a dashed line versus a solid line in graphical solutions?
Use a dashed line for strict inequalities (< or >) to show that points on the line are not part of the solution, and a solid line for non-strict inequalities (≤ or ≥).
How do I find the half-plane to shade in a two-variable inequality?
Test a point not on the line (like origin (0,0)). If it satisfies the inequality, shade the region containing that point; otherwise, shade the opposite region.
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