Subjects

Arithmetic

Absolute Value

Comparing Absolute Values

Learn How to Compare Absolute Values on a Number Line!

Name: Knowunity
Brand: Knowunity

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Learn How to Compare Absolute Values on a Number Line!

Islombek

@islombek_zqdd

105 Followers

Understanding the concept of absolute value in mathematics is essential for comparing distances on a number line and solving inequalities. This comprehensive guide explores absolute value comparisons, inequalities, and real-world applications.

Learn how to compare absolute values on a number line by focusing on distances from zero
Master techniques for solving absolute value inequalities with examples through two-case analysis
Understand the practical applications of absolute values in measuring magnitudes and distances
Explore step-by-step methods for placing and comparing absolute values on number lines
Discover how to interpret absolute values in various mathematical and real-world contexts

8/12/2023

Comparing absolute values on the number line:
• When comparing absolute values on the number line, it's
important to understand that the abs

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Testing Solutions to Absolute Value Inequalities

This section delves into solving absolute value inequalities through systematic testing and analysis. The content covers the two-case method and provides detailed examples of inequality solutions.

Example: For the inequality |x - 3| < 5, we solve two cases:

x - 3 < 5 (leading to x < 8)
-(x - 3) < 5 (leading to x > -2)

Highlight: When solving absolute value inequalities, always consider both positive and negative possibilities to find the complete solution set.

Definition: An absolute value inequality solution represents all values that satisfy the given condition when considering both positive and negative cases.

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Interpreting and Applying Absolute Values

This final section explores the practical interpretation and application of absolute values in various contexts. The content connects mathematical concepts to real-world scenarios and provides comprehensive examples.

Example: A person walking 10 meters forward and 10 meters backward covers a total distance of 20 meters, though their displacement is zero, demonstrating how absolute values measure actual distance traveled.

Highlight: Absolute values have practical applications in measuring distances, errors in scientific measurements, and temperature differences.

Vocabulary: Displacement refers to the overall change in position, while distance refers to the total path length traveled, regardless of direction.

Definition: In real-world applications, absolute value represents the magnitude of a quantity without regard to its direction or sign.

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Comparing Absolute Values on the Number Line

This section introduces fundamental concepts of absolute values and their representation on a number line. The content explains how absolute values represent distances from zero, regardless of sign, and demonstrates comparison techniques.

Definition: The absolute value of a number represents its distance from zero on the number line, regardless of whether the number is positive or negative.

Example: When comparing -5 and 3, their absolute values are 5 and 3 respectively, showing that |-5| is greater than |3| because 5 is further from zero than 3.

Highlight: When placing absolute values on the number line, always convert negative numbers to their positive equivalents to represent the true distance from zero.

Vocabulary: Magnitude refers to the size or absolute value of a number, ignoring its sign.

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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.

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

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Students use Knowunity

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In Education App Charts in 12 Countries

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

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

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Subjects

Arithmetic

Absolute Value

Comparing Absolute Values

Learn How to Compare Absolute Values on a Number Line!

Islombek

@islombek_zqdd

105 Followers

Learn how to compare absolute values on a number line by focusing on distances from zero
Master techniques for solving absolute value inequalities with examples through two-case analysis
Understand the practical applications of absolute values in measuring magnitudes and distances
Explore step-by-step methods for placing and comparing absolute values on number lines
Discover how to interpret absolute values in various mathematical and real-world contexts

8/12/2023

6th/7th

Arithmetic

Testing Solutions to Absolute Value Inequalities

This section delves into solving absolute value inequalities through systematic testing and analysis. The content covers the two-case method and provides detailed examples of inequality solutions.

Example: For the inequality |x - 3| < 5, we solve two cases:

x - 3 < 5 (leading to x < 8)
-(x - 3) < 5 (leading to x > -2)

Highlight: When solving absolute value inequalities, always consider both positive and negative possibilities to find the complete solution set.

Definition: An absolute value inequality solution represents all values that satisfy the given condition when considering both positive and negative cases.

Interpreting and Applying Absolute Values

Example: A person walking 10 meters forward and 10 meters backward covers a total distance of 20 meters, though their displacement is zero, demonstrating how absolute values measure actual distance traveled.

Highlight: Absolute values have practical applications in measuring distances, errors in scientific measurements, and temperature differences.

Vocabulary: Displacement refers to the overall change in position, while distance refers to the total path length traveled, regardless of direction.

Definition: In real-world applications, absolute value represents the magnitude of a quantity without regard to its direction or sign.

Comparing Absolute Values on the Number Line

Definition: The absolute value of a number represents its distance from zero on the number line, regardless of whether the number is positive or negative.

Example: When comparing -5 and 3, their absolute values are 5 and 3 respectively, showing that |-5| is greater than |3| because 5 is further from zero than 3.

Highlight: When placing absolute values on the number line, always convert negative numbers to their positive equivalents to represent the true distance from zero.

Vocabulary: Magnitude refers to the size or absolute value of a number, ignoring its sign.

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.

Download in

Google Play

Download in

App Store

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