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Modeling with Linear Inequalities

Using Inequalities for Real-Life Problems: Math Fun with Elevator Limits

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Using Inequalities for Real-Life Problems: Math Fun with Elevator Limits
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JD

@babyfacejordan1

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Subject Expert

Using inequalities to represent real-world situations is essential for solving mathematical problems involving constraints and limitations. Here's a comprehensive analysis of the content.

A comprehensive guide to understanding and solving inequalities, focusing on algebraic inequalities in elevator weight limits and other practical applications. The material covers how to represent constraints mathematically and interpret solutions.

Key points:

  • Understanding inequality symbols and their meanings in mathematical contexts
  • Applying inequalities to real-world scenarios like elevator capacity limits
  • Solving one-variable inequalities using various methods
  • Interpreting inequality symbols in math equations for practical problem-solving

5/12/2023

116

Lesson 18: Representing Situations with Inequalities • Let's use inequalities to represent constraints in situations. 18.1: What Do Those Sy

View

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.

Lesson 18: Representing Situations with Inequalities • Let's use inequalities to represent constraints in situations. 18.1: What Do Those Sy

View

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.

Lesson 18: Representing Situations with Inequalities • Let's use inequalities to represent constraints in situations. 18.1: What Do Those Sy

View

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.

Lesson 18: Representing Situations with Inequalities • Let's use inequalities to represent constraints in situations. 18.1: What Do Those Sy

View

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.

Lesson 18: Representing Situations with Inequalities • Let's use inequalities to represent constraints in situations. 18.1: What Do Those Sy

View

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.

Lesson 18: Representing Situations with Inequalities • Let's use inequalities to represent constraints in situations. 18.1: What Do Those Sy

View

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.

Lesson 18: Representing Situations with Inequalities • Let's use inequalities to represent constraints in situations. 18.1: What Do Those Sy

View

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.

Lesson 18: Representing Situations with Inequalities • Let's use inequalities to represent constraints in situations. 18.1: What Do Those Sy

View

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.

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These notes explain inequalities, how to graph them, and solve them.

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Subjects

/

Algebra 1

/

Inequalities

/

Modeling with Linear Inequalities

Using Inequalities for Real-Life Problems: Math Fun with Elevator Limits

user profile picture

JD

@babyfacejordan1

·

9 Followers

Follow

Subject Expert

Using inequalities to represent real-world situations is essential for solving mathematical problems involving constraints and limitations. Here's a comprehensive analysis of the content.

A comprehensive guide to understanding and solving inequalities, focusing on algebraic inequalities in elevator weight limits and other practical applications. The material covers how to represent constraints mathematically and interpret solutions.

Key points:

  • Understanding inequality symbols and their meanings in mathematical contexts
  • Applying inequalities to real-world scenarios like elevator capacity limits
  • Solving one-variable inequalities using various methods
  • Interpreting inequality symbols in math equations for practical problem-solving

5/12/2023

116

 

9th/6th

 

Algebra 1

1

Lesson 18: Representing Situations with Inequalities • Let's use inequalities to represent constraints in situations. 18.1: What Do Those Sy

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Access to all documents

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Join milions of students

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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.

Lesson 18: Representing Situations with Inequalities • Let's use inequalities to represent constraints in situations. 18.1: What Do Those Sy

Sign up to see the content. It's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

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.

Lesson 18: Representing Situations with Inequalities • Let's use inequalities to represent constraints in situations. 18.1: What Do Those Sy

Sign up to see the content. It's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

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.

Lesson 18: Representing Situations with Inequalities • Let's use inequalities to represent constraints in situations. 18.1: What Do Those Sy

Sign up to see the content. It's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

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.

Lesson 18: Representing Situations with Inequalities • Let's use inequalities to represent constraints in situations. 18.1: What Do Those Sy

Sign up to see the content. It's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

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.

Lesson 18: Representing Situations with Inequalities • Let's use inequalities to represent constraints in situations. 18.1: What Do Those Sy

Sign up to see the content. It's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

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.

Lesson 18: Representing Situations with Inequalities • Let's use inequalities to represent constraints in situations. 18.1: What Do Those Sy

Sign up to see the content. It's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

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.

Lesson 18: Representing Situations with Inequalities • Let's use inequalities to represent constraints in situations. 18.1: What Do Those Sy

Sign up to see the content. It's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

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.

Similar Content

Algebra 1 - Solving Linear Inequalities

Shows how to graph a linear inequality and how to tell if a given point on a graph is a solution.

348

812

0

Know Solving Linear Inequalities thumbnail

Algebra 1 - Linear Inequalities - Algebra

These notes explain inequalities, how to graph them, and solve them.

1

200

0

Know Linear Inequalities - Algebra thumbnail

Can't find what you're looking for? Explore other subjects.

Knowunity is the # 1 ranked education app in five European countries

Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.

Ranked #1 Education App

Download in

Google Play

Download in

App Store

Knowunity is the # 1 ranked education app in five European countries

4.9+

Average App Rating

15 M

Students use Knowunity

#1

In Education App Charts in 12 Countries

950 K+

Students uploaded study notes

Still not sure? Look at what your fellow peers are saying...

iOS User

I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D

Stefan S, iOS User

The application is very simple and well designed. So far I have found what I was looking for :D

SuSSan, iOS User

Love this App ❤️, I use it basically all the time whenever I'm studying