Class 11 Maths - TELANGANA
Linear Inequalities
The 'Linear Inequalities' chapter in Class 11 Mathematics builds a crucial foundation for higher-level algebra and optimization techniques like linear programming. Students learn to solve algebraic inequalities in one and two variables, representing their solutions graphically on a number plane. Understanding open and closed half-planes, strict versus slack inequalities, and system of inequalities is essential. For the Telangana State Board of Secondary Education (TSBSE) exams, mastering this chapter ensures you can secure high-scoring marks in both short-answer and long-answer sections by carefully following graphing and shading rules.
Start Learning FreeKey Concepts
Inequality
A mathematical statement involving symbols like <, >, <=, or >=, showing that one expression is greater than or less than another.
Linear Inequality in One Variable
An inequality of the form ax + b < 0 (or <=, >, >=) where a != 0, which has solutions represented on a number line.
Linear Inequality in Two Variables
An inequality of the form ax + by < c, whose solutions form a region on the Cartesian plane called a half-plane.
Graphical Solution
The representation of all solutions of a linear inequality in two variables as a shaded region on a graph, bounded by a dashed or solid line.
System of Inequalities
A set of two or more linear inequalities considered simultaneously, where the solution region is the common overlapping area of all individual inequalities.
Important Formulas
Board Exam Info
In the Telangana (TSBSE) Class 11 Mathematics examinations, this chapter typically carries around 4 to 6 marks. Common question types include solving algebraic linear inequalities in one variable, finding the solution set of a system of linear inequalities graphically, and word problems involving practical constraints.
Frequently Asked Questions
When should I use a dashed line versus a solid line in graphing?
Use a dashed (broken) line for strict inequalities (< or >) to show that points on the line are not included in the solution. Use a solid line for slack inequalities (<= or >=) to show that the boundary line is included.
How do I know which side of the line to shade?
Pick a test point not on the line (usually the origin, (0,0)). Substitute its coordinates into the inequality. If the statement is true, shade the side containing the test point; if false, shade the opposite side.
What happens to the inequality sign when multiplying or dividing by a negative number?
The inequality sign reverses (e.g., if -2x > 6, dividing by -2 gives x < -3).
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