Pure: Inequalities

A. Inequality Definition: An inequality is a mathematical statement that compares two expressions using an inequality symbol (>, <, ≥, ≤, ≠). Explanation: Unlike an equation which states that two expressions are equal, an inequality states that one expression is greater than, less than, greater than or equal to, or less than or equal to another. It helps describe a range of possible values rather than a single specific value, indicating a relationship of order or size between two quantities. Think of it as: Think of a weighing scale. If the scale is balanced, it's an equation. If one side is heavier or lighter, it's an inequality, showing a difference in weight or quantity. Real-world application: Inequalities are used when setting speed limits (e.g., speed ≤ 60 km/h), calculating safe load capacities for bridges (e.g., load ≤ 5000 kg), or determining minimum passing grades in exams (e.g., score ≥ 35%). B. Trichotomy Law Definition: For any two real numbers, x and y, exactly one of the following three relationships must be true: x > y, x < y, or x = y.