Class 11 Maths Chapter 5 Linear Inequalities Revision Notes
In real life, many situations are defined by limits rather than exact values. A student may need to score at least 75% to qualify for a scholarship, a machine may operate below a certain temperature, or a product price may remain less than a fixed budget. Such conditions cannot be represented using equations alone—they require Linear Inequalities. This chapter introduces mathematical techniques to express, solve, and interpret inequalities involving one or two variables. Understanding solution sets, interval notation, graphical representation, and feasible regions forms the basis for optimization and higher mathematical modelling. These concepts are frequently tested in JEE Main, JEE Advanced, and CBSE Board examinations.
At ALLEN, our expert faculty have prepared these Class 11 Maths Chapter 5: Linear Inequalities Revision Notes to make every concept simple, logical, and exam-oriented. These notes include concise theory, graphical methods, interval notation, important properties, shortcut techniques, solved examples, and previous year question trends to help you revise efficiently. Whether you're building your fundamentals or preparing for competitive examinations, these revision notes will strengthen your conceptual understanding and improve your speed and accuracy while solving inequality-based problems.
1.0Chapter Snapshot
2.0Related Supporting Study Resources
3.0Learning Outcomes
After completing these revision notes, you will be able to:
- Understand the concept of linear inequalities and inequality symbols.
- Solve linear inequalities involving one variable.
- Represent solution sets using interval notation.
- Plot solutions of inequalities on the number line.
- Solve linear inequalities in two variables graphically.
- Identify feasible regions for systems of inequalities.
- Apply linear inequalities to solve JEE and CBSE-level problems.
- Develop a foundation for Linear Programming and Optimization.
4.05-Minute Quick Revision
Must-Revise Concepts
- Inequality symbols
- Linear inequalities
- Solution set
- Interval notation
- Open and closed intervals
- Number line representation
- Linear inequalities in two variables
- Half planes
- Feasible region
- Systems of inequalities
Important Formula Recall
- If (a>b), then (a+c>b+c)
- If (a>b) and (c>0), then (ac>bc)
- If (a>b) and (c<0), then (ac<bc) (inequality reverses)
- Open Interval: ((a,b))
- Closed Interval: ([a,b])
- Semi-open Intervals: ((a,b]), ([a,b))
Important Properties
- Adding or subtracting the same number preserves the inequality.
- Multiplying or dividing by a negative number reverses the inequality sign.
- Solutions of two-variable inequalities lie in half-planes.
- The common shaded region represents the feasible solution.
- Boundary lines are included only when the inequality contains ≤ or ≥.
5.0High Weightage Topics
6.0Formula Handbook
The following formulas and standard results are essential for solving questions from Linear Inequalities in JEE Main, JEE Advanced, and CBSE examinations.
7.0Common Mistakes & JEE Tips
Linear Inequalities is a straightforward yet highly scoring chapter. Most mistakes occur due to sign errors, incorrect interval notation, or improper graphical representation. Paying attention to basic rules can significantly improve accuracy.
8.0ALLEN Faculty Tips
- Memorize the rule that multiplying or dividing by a negative number reverses the inequality sign.
- Practice interval notation until it becomes intuitive.
- Always test a point to identify the correct half-plane.
- Draw neat graphs with proper boundary lines.
- Revise feasible region concepts before starting Linear Programming.
- Solve graphical problems regularly to improve speed and confidence.
- Practice Previous Years' Questions to understand common examination patterns.
9.0PYQ Trend Analysis
Linear Inequalities is a moderate-weightage chapter that forms the foundation for Linear Programming and graphical optimization problems. Questions generally test conceptual understanding of inequality rules, interval notation, graphical representation, and feasible regions.
Note: The trend below is based on the analysis of previous years' JEE Main and JEE Advanced question papers. The exact number of questions may vary each year.
10.0Most Common Question Types
- Solving linear inequalities in one variable.
- Writing solution sets in interval notation.
- Representing inequalities on the number line.
- Solving systems of linear inequalities.
- Identifying feasible regions graphically.
- Determining whether a point satisfies a given inequality.
- Application-based questions involving constraints and optimization.
11.0Smart Revision Strategy
Follow this sequence to revise the chapter efficiently before examinations:
- Revise the basic properties of inequalities.
- Practice solving one-variable inequalities.
- Learn interval notation thoroughly.
- Revise number line representation.
- Solve graphical problems involving two variables.
- Practice feasible region questions.
- Solve Previous Years' Questions (PYQs).
- Finish with mixed conceptual and application-based problems under timed conditions