Linear Inequation
ICSE · Class 10 · Mathematics
Quick revision notes for Linear Inequation — ICSE Class 10 Mathematics. Key concepts, formulas, and definitions for last-minute revision.
Key Topics to Revise
Basic Concepts and Definitions
- An inequation is a mathematical statement comparing two expressions using inequality symbols
- Linear inequations involve variables with degree 1 only
- The general form is ax + b > 0, ax + b < 0, ax + b ≥ 0, or ax + b ≤ 0 where a ≠ 0
Interval Notation and Number Line Representation
- Open interval (a, b): excludes endpoints a and b, shown with hollow circles
- Closed interval [a, b]: includes endpoints a and b, shown with filled circles
- Semi-open intervals (a, b] or [a, b): include one endpoint only
Rules for Solving Linear Inequations
- Addition-Subtraction Rule: Same operation on both sides maintains inequality direction
- Multiplication-Division by positive number: Inequality direction remains same
- Multiplication-Division by negative number: Inequality direction reverses
Solving Linear Inequations - Step by Step Method
- Step 1: Simplify both sides by removing brackets and combining like terms
- Step 2: Move all variable terms to one side and constants to other side
- Step 3: Apply multiplication/division rule carefully (watch for negative coefficients)
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