Linear Inequalities — Chapter Summary
Punjab Board · Class 11 · Mathematics
Summary of Linear Inequalities for Punjab Board Class 11 Mathematics. Part of the Punjab Board Class 11 Mathematics syllabus.
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Overview
Linear inequalities are mathematical statements that use comparison symbols (<, >, ≤, ≥) instead of equality signs to show relationships between expressions. Unlike equations that show exact equality, inequalities show ranges of values that satisfy a condition. This chapter focuses on solving linear
Key Concepts
An inequality is a mathematical statement
An inequality is a mathematical statement that shows the relationship between two quantities using symbols: < (less than), > (greater than), ≤ (less t
Strict inequalities use < or >
Strict inequalities use < or > and do NOT include the boundary value. Slack inequalities use ≤ or ≥ and DO include the boundary value. For example, x
You can add or subtract
You can add or subtract the same number from both sides of an inequality without changing the inequality sign. If a < b, then a + c < b + c for any re
When multiplying or dividing both sides
When multiplying or dividing both sides by a POSITIVE number, the inequality sign stays the same: if a < b and c > 0, then ac < bc. However, when mult
These are inequalities of the form
These are inequalities of the form ax + b < c, ax + b > c, ax + b ≤ c, or ax + b ≥ c, where a ≠ 0. The solution is found by isolating x using the rule
Learning Objectives
- Understand the concept of inequalities and their differences from equations
- Solve linear inequalities in one variable algebraically and represent solutions graphically
- Apply rules for solving inequalities, especially when multiplying or dividing by negative numbers
- Solve systems of linear inequalities and represent solutions on a number line
- Solve double inequalities (compound inequalities) with proper algebraic manipulation
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Sources & Official References
Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.
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