Class 11 Maths - CBSE
Linear Inequalities
The Chapter Linear Inequalities in Class 11 Mathematics builds upon the foundation of linear equations by introducing inequalities involving two variables and systems of inequalities. Students learn to represent statements mathematically using inequality symbols like <, >, ≤, and ≥. This chapter covers algebraic solutions in one and two variables and graphical representations on a Cartesian plane. It is crucial for board exams as it forms the basis for Linear Programming, a high-weightage topic in Class 12. Mastering this chapter ensures strong problem-solving skills for both school assessments and competitive exams like JEE.
Start Learning FreeKey Concepts
Algebraic Solutions in One Variable
Finding the range of real numbers that satisfy a linear inequality in a single variable by performing algebraic operations without changing the inequality sign.
Graphical Solution in Two Variables
Representing a linear inequality in two variables on a Cartesian plane by drawing a boundary line and shading the appropriate half-plane determined by a test point.
Strict vs Slack Inequalities
Strict inequalities use < or > and are represented graphically by dashed boundary lines, whereas slack inequalities use ≤ or ≥ and are represented by solid lines.
System of Linear Inequalities
A set of two or more simultaneous linear inequalities whose common overlapping region on the graph represents the simultaneous solution set.
Important Formulas
Board Exam Info
In CBSE Class 11 Mathematics exams, this chapter typically carries around 4 to 6 marks under the Algebra unit. Common question types include solving algebraic inequalities in one variable and showing the solution on a number line, solving a system of linear inequalities graphically, and word problems involving real-life constraints.
Frequently Asked Questions
Why does the inequality sign reverse when multiplying or dividing by a negative number?
Multiplying or dividing a negative number flips its position relative to zero on the number line, effectively reversing the direction of comparison between the two values.
How do I know which side of the line to shade in a two-variable inequality?
Choose a test point not on the line (usually origin 0,0) and substitute its coordinates into the inequality. If the statement is true, shade the side containing the test point; if false, shade the opposite side.
When should I use a dashed line versus a solid line in graphical solutions?
Use a dashed 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 points on the line are included.
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