Page 2: Elevator Weight and Capacity Constraints

This page demonstrates how to apply inequalities to real-world situations using an elevator scenario with multiple constraints.

Example: An elevator car with maximum capacity of 15 people and 1,500 kg weight limit, considering different weights for adults and children.

Vocabulary: Variables are defined clearly: p = number of people, a = number of adults, c = number of children, W = weight of elevator.

Highlight: The problem introduces multiple constraints that must be satisfied simultaneously: a + c ≤ 15 and 70a + 35c + 4a + 4c ≤ 1500.

Page 3: Understanding Inequality Relationships

This page provides a comprehensive summary of how inequalities are used to represent various relationships and constraints.

Definition: Inequalities express relationships where one quantity is greater than or less than another using symbols <, ≤, >, or ≥.

Example: Complex real-world applications include:

• Rectangle area constraints: A ≤ 100
• Ticket sales requirements: d + e > 4,000
• Working hours limitations: 5 < h ≤ 20

Highlight: The page emphasizes how inequalities can express both simple number relationships and complex real-world constraints.

Page 7: Practical Applications

This page presents real-world problems involving inequalities.

Example: Drama club dinner budget problem with multiple constraints.

Highlight: Demonstrates how to translate real-world situations into mathematical inequalities.