Mathematics · Class 11
Linear Inequalities
Learn Linear Inequalities with notes, examples, and practice questions.
3 sections15–25 min read6 MCQs · 2 examples
Chapter Overview
Linear inequalities in one or two variables describe half-planes and intervals. Solving them is algebra with careful sign reversal when multiplying by negatives.
Rules
- Adding/subtracting same number: inequality direction unchanged
- Multiply/divide by negative: flip inequality sign
- Number line: open circle for <, closed for ≤
Two Variables
- ax + by < c → half-plane
- Graph boundary line; test point for shading
- System → intersection of half-planes
Solved Examples
Step-by-step solutions — read each step before checking the final answer.
Solve 3x−7<8
Find solution set.
- 13x<15
- 2x<5
Answer
(−∞, 5)
Graph 2x+y≤4
Describe region.
- 1Line 2x+y=4
- 2Test (0,0): 0≤4 true → shade toward origin
Answer
Half-plane including origin
Key Points to Remember
- ✓ Interval notation for 1D
- ✓ Feasible region for LPP preview
- ✓ Modulus inequalities split into cases
Exam Tips
- • Flip sign when multiplying by negative
- • Shade correctly on graph
Practice MCQs — Linear Inequalities
Test your understanding with topic-wise multiple choice questions. Explanations appear after each answer.
Question 1 of 6Score: 0/0
Multiply inequality by −2: