Class 11 Maths - KERALA
Linear Inequalities
The chapter 'Linear Inequalities' in Class 11 Mathematics under the Kerala SCERT syllabus introduces students to algebraic expressions connected by inequality symbols like <, >, ≤, and ≥. Building upon basic linear equations, this chapter teaches how to solve linear inequalities in one variable and two variables algebraically and graphically. It is a foundational topic that extends into Linear Programming in Class 12, making it crucial for board exams. Students learn to represent solution regions on a Cartesian plane, which frequently appears in both short-answer and essay-type questions in the terminal examinations.
Start Learning FreeKey Concepts
Inequality
A mathematical statement comparing two expressions using inequality symbols such as <, >, ≤, or ≥.
Linear Inequality in One Variable
An inequality of the form ax + b < 0 (or with other inequality symbols) where a ≠ 0, solved by isolating the variable.
Linear Inequality in Two Variables
An inequality involving two variables, like ax + by ≤ c, whose solution set is a half-plane in the Cartesian coordinate system.
Graphical Solution
The method of representing solutions of inequalities in two variables by shading the appropriate half-plane on a graph after drawing a boundary line.
Rules for Solving Inequalities
Fundamental algebraic rules, notably that multiplying or dividing both sides by a negative number reverses the direction of the inequality sign.
Important Formulas
Board Exam Info
In the Kerala SCERT Class 11 Mathematics board examinations, this chapter typically carries around 4 to 6 marks. Questions usually include solving a linear inequality in one variable and representing its solution on a number line, or finding the graphical solution of a system of linear inequalities in two variables.
Frequently Asked Questions
When you multiply or divide a negative inequality statement (like -2 < 3) by a negative number, the relative positions on the number line flip, making the inequality symbol reverse (e.g., 2 > -3).
When you multiply or divide both sides of an inequality by a negative number, the order of numbers is reversed, which forces the inequality symbol to flip direction.
Use a dashed line for strict inequalities (< or >) to show that the points on the line are not included in the solution. Use a solid line for inclusive inequalities (≤ or ≥) to show that the points on the line are included.
Use a dashed line for < and >, and a solid line for ≤ and ≥.
Pick a test point (usually the origin, (0, 0)) that does not lie on the line. Substitute its coordinates into the inequality; if it makes the statement true, shade the region containing that point. If false, shade the opposite region.
Substitute a test point like (0, 0) into the inequality; if the statement is true, shade the side containing the point, otherwise shade the other side.
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