Class 11 Maths - ANDHRA-PRADESH
Linear Inequalities
The chapter Linear Inequalities in Class 11 Mathematics builds upon the foundation of linear equations to introduce expressions involving inequality symbols like less than, greater than, or equal to. Students learn to solve linear inequalities in one and two variables algebraically and represent their solutions graphically on a number line or coordinate plane. This chapter is vital for the Andhra Pradesh Board of Secondary Education (BSEAP) examinations as it forms the basis for Linear Programming, a high-weightage topic in higher classes, and frequently appears in both short-answer and long-answer board exam questions.
Start Learning FreeKey Concepts
Inequality
A statement involving variables and real numbers connected by inequality signs such as <, >, ≤, or ≥.
Algebraic Solutions in One Variable
Finding all the real values of a variable that satisfy a given linear inequality using standard algebraic operations.
Graphical Representation on Number Line
Visualizing the solution set of a linear inequality in one variable by shading the corresponding region on a number line.
Graphical Solutions in Two Variables
Finding the half-plane that satisfies a linear inequality in two variables by plotting the boundary line and testing a point.
System of Linear Inequalities
Solving a set of two or more simultaneous linear inequalities by finding the common overlapping region of their individual solutions.
Important Formulas
Board Exam Info
In the Andhra Pradesh (BSEAP) Class 11 Mathematics board examinations, the chapter on Linear Inequalities typically carries around 4 to 6 marks. Common question types include solving linear inequalities in one variable algebraically and representing the solution on a number line, as well as finding the graphical solution region for a system of linear inequalities in two variables.
Frequently Asked Questions
Why does the inequality sign reverse when multiplying or dividing by a negative number?
Multiplying or dividing by a negative number reflects the numbers across zero on the number line, which reverses their relative order (for example, -2 < 3, but multiplying by -1 gives 2 > -3).
What is the difference between open and closed circles on a number line graph?
An open circle is used for strict inequalities (< or >) to show the endpoint is not included, while a solid closed circle is used for inclusive inequalities (≤ or ≥) to show the endpoint is included.
How do we choose which half-plane to shade when graphing a two-variable inequality?
You pick a test point not on the line (usually the origin, 0,0) and substitute its coordinates into the inequality; if the statement is true, shade the side containing the test point, otherwise shade the opposite side.
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