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 4: Practical Applications in Field Trip Planning

This page applies inequality concepts to a real-world scenario involving field trip cost comparisons.

Example: Two orchards with different pricing structures:

• Orchard A: $9 per person with 3 chaperones required
• Orchard B: $10 per person with 1 chaperone required

Highlight: Students learn to compare costs using inequalities for different class sizes.

Page 5: Solving and Testing Inequalities

This page focuses on solving inequalities and verifying solutions through testing.

Vocabulary: Solution verification involves testing values on both sides of the solution point.

Example: When solving 4$x + 3$/5, students test values both less than and greater than x = 2 to verify the solution.

Highlight: The importance of checking multiple values to confirm inequality solutions is emphasized.

Page 5: Solving Inequalities

This page focuses on solving inequalities and comparing them with equations.

Example: Detailed solution process for 4$x + 3$ ≤ 4x - 12

Highlight: The importance of testing multiple values to verify solutions to inequalities.

Page 6: Solution Sets

This page explains the concept of solution sets for inequalities.

Definition: A solution set includes all values that make an inequality true.

Example: For t/2 > 10, values like 30 and 48 are solutions because they satisfy the inequality.

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.

Page 1: Introduction to Inequality Symbols

This page introduces the basic concepts of inequalities and their symbols, focusing on how to interpret and use them correctly in mathematical expressions.

Definition: Inequality symbols represent relationships where values can be greater than, less than, or equal to other values.

Example: In the expression h > 50, h must be greater than 50, while in h ≤ 20, h must be less than or equal to 20.

Highlight: Students learn to test specific values (25, 30, 40) to determine if they are solutions to given inequalities.