Class 11 Maths - UP
Linear Inequalities
The Chapter 'Linear Inequalities' in Class 11 Mathematics introduces students to mathematical expressions involving 'less than', 'greater than', or their combinations, rather than strict equality. Building upon linear equations from earlier classes, this chapter teaches how to solve linear inequalities in one and two variables algebraically and represent their solution regions graphically on a Cartesian plane. Mastery of this topic is crucial for UPMSP board exams as it forms the foundational base for Linear Programming in Class 12, making it a high-scoring and conceptually vital area for students preparing for higher mathematics.
Start Learning FreeKey Concepts
Inequality
A statement involving symbols like <, >, ≤, or ≥ comparing two real numbers or algebraic expressions.
Linear Inequality in One Variable
An inequality of the form ax + b < 0 (or ≤, >, ≥) where a ≠ 0, solved by isolating the variable using algebraic rules.
Linear Inequality in Two Variables
An inequality of the form ax + by < c representing a region on the Cartesian plane bounded by a straight line.
Graphical Solution
The method of shading the half-plane that satisfies a given linear inequality in two variables, determined by testing a point like (0, 0).
System of Linear Inequalities
A set of two or more simultaneous inequalities whose common overlapping solution region represents the final answer.
Important Formulas
Board Exam Info
In the Uttar Pradesh (UPMSP) Class 11 Mathematics examinations, this chapter typically carries around 4 to 6 marks. Common question types include solving algebraic inequalities in one variable and showing 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 both sides of an inequality by a negative number reflects the numbers across zero on the number line, which inverts the order of magnitude, hence reversing the inequality sign.
How do I know which side of the line to shade in graphical inequalities?
Choose a test point not on the line (usually the origin, 0, 0). Substitute its coordinates into the inequality; if it makes the statement true, shade the region containing that point, otherwise shade the opposite side.
What is the difference between strict and slack inequalities?
Strict inequalities use '<' or '>' and are represented by dashed lines on a graph. Slack inequalities use '≤' or '≥' and are represented by solid lines to show that points on the boundary line are included in the solution.
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