Class 11 Maths - PUNJAB
Linear Inequalities
The chapter 'Linear Inequalities' in Class 11 Mathematics introduces students to algebraic statements involving inequalities rather than equations. You will learn to solve linear inequalities in one and two variables, represent solutions on a number line, and solve graphical systems of linear inequalities. This is a foundational chapter for higher-level mathematics and linear programming. In the Punjab (PSEB) board exams, questions from this chapter frequently appear as short-answer problems and long-answer graphical questions, making it a high-scoring section that requires careful attention to rules such as reversing the inequality sign when multiplying or dividing by a negative number.
Start Learning FreeKey Concepts
Inequality
A mathematical statement comparing two expressions using symbols like <, >, ≤, or ≥ instead of an equals sign.
Linear Inequality in One Variable
An inequality of the form ax + b < 0 (or ≤, >, ≥) where x is the variable and a ≠ 0, solved by isolating x on one side.
Rules for Solving Inequalities
Equal numbers can be added or subtracted, and both sides can be multiplied or divided by a positive number without changing the sign, but multiplying or dividing by a negative number reverses the inequality sign.
Graphical Solution in Two Variables
Representing the solution region of an inequality like ax + by ≤ c on a Cartesian plane using a solid or dashed boundary line and a test point.
System of Linear Inequalities
A set of two or more linear inequalities considered together, where the solution region is the common overlapping area of all individual inequalities.
Important Formulas
Board Exam Info
In the Punjab (PSEB) Class 11 Mathematics board exams, Linear Inequalities typically carries around 4 to 6 marks. Common question types include solving algebraic inequalities in one variable for real numbers, and finding the graphical solution region for a system of two or three linear inequalities in a 2D plane.
Frequently Asked Questions
Why does the inequality sign reverse when multiplying or dividing by a negative number?
Because multiplying a negative number across an inequality flips its position relative to zero on the number line, changing which value is larger (for example, -2 < -3 is false, but 2 > 3 is false while -2 > -3 is true when compared properly).
How do I know whether to draw a solid or dashed line for graphical inequalities?
Use a solid line when the inequality includes 'less than or equal to' (≤) or 'greater than or equal to' (≥) to show that points on the line are included. Use a dashed line for strict inequalities (< or >) to show the line is not included.
How do I select which side of the line to shade in a graph?
Pick a test point not on the line (usually the origin, (0,0)) and substitute its coordinates into the inequality. If the resulting statement is true, shade the side containing that point; if false, shade the opposite side.
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