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Intro to Systems of Equations

Easy Steps for Solving Compound Inequalities and Absolute Value Problems

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Easy Steps for Solving Compound Inequalities and Absolute Value Problems
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Clara Vandenbelt

@clara_tiara0

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110 Followers

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A comprehensive guide to solving compound inequalities examples and solutions and absolute value equations step by step, covering essential mathematical concepts and problem-solving techniques.

  • Learn to identify and solve compound inequalities using 'and' and 'or' operations
  • Master absolute value equations step by step through detailed examples
  • Understand how to solve absolute value inequalities problems using number lines
  • Practice with real-world applications and multiple solution methods
  • Explore the relationship between absolute values and distance from zero
  • Gain proficiency in handling both positive and negative solutions

10/23/2023

67

J I I I I J J J J 2 e 1-6 Compound Inequalities. • 2 types of compound inequalities, or & and or and ← + -3 -2 x=-1 Dr x21 -3 -2 "1 Example

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Page 2: Absolute Value Equations and Inequalities

This page delves into the concept of absolute value equations and inequalities, providing comprehensive explanations and multiple solution methods.

Definition: Absolute value represents the distance from zero on a number line, always resulting in a positive value or zero.

Example: In solving |x + 5| = 2, two cases must be considered:

  1. Positive case: x + 5 = 2
  2. Negative case: x + 5 = -2

Highlight: When solving absolute value equations, always consider both positive and negative possibilities to find all valid solutions.

Example: For 2|x + 5| = 4:

  1. Simplify to |x + 5| = 2
  2. Solve for x + 5 = 2 and x + 5 = -2
  3. Solutions are x = -3 and x = -7

Vocabulary: The term "no solution" indicates when an absolute value equation has no real number solutions that satisfy the given conditions.

J I I I I J J J J 2 e 1-6 Compound Inequalities. • 2 types of compound inequalities, or & and or and ← + -3 -2 x=-1 Dr x21 -3 -2 "1 Example

View

Page 1: Compound Inequalities

This page introduces the fundamental concepts of compound inequalities and their solutions. The content focuses on two main types of compound inequalities: 'and' and 'or' operations, with detailed explanations of how to solve them.

Definition: Compound inequalities are mathematical statements that combine two or more inequalities using 'and' or 'or' operations.

Example: For the inequality -3≤x≤3, x must be greater than or equal to -3 AND less than or equal to 3.

Highlight: When solving compound inequalities with 'and', the solution must satisfy both conditions simultaneously.

The page demonstrates step-by-step solutions for various compound inequalities:

Example: Solving -3x+2>-7:

  1. Add 2 to both sides: -3x>-9
  2. Divide by -3: x<3

Vocabulary: The term "middle" refers to the value of x that must fall between two boundary points in an 'and' compound inequality.

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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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SuSSan, iOS User

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

Subjects

/

Arithmetic

/

Systems of Equations

/

Intro to Systems of Equations

Easy Steps for Solving Compound Inequalities and Absolute Value Problems

user profile picture

Clara Vandenbelt

@clara_tiara0

·

110 Followers

Follow

A comprehensive guide to solving compound inequalities examples and solutions and absolute value equations step by step, covering essential mathematical concepts and problem-solving techniques.

  • Learn to identify and solve compound inequalities using 'and' and 'or' operations
  • Master absolute value equations step by step through detailed examples
  • Understand how to solve absolute value inequalities problems using number lines
  • Practice with real-world applications and multiple solution methods
  • Explore the relationship between absolute values and distance from zero
  • Gain proficiency in handling both positive and negative solutions

10/23/2023

67

 

8th

 

Arithmetic

6

J I I I I J J J J 2 e 1-6 Compound Inequalities. • 2 types of compound inequalities, or & and or and ← + -3 -2 x=-1 Dr x21 -3 -2 "1 Example

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 2: Absolute Value Equations and Inequalities

This page delves into the concept of absolute value equations and inequalities, providing comprehensive explanations and multiple solution methods.

Definition: Absolute value represents the distance from zero on a number line, always resulting in a positive value or zero.

Example: In solving |x + 5| = 2, two cases must be considered:

  1. Positive case: x + 5 = 2
  2. Negative case: x + 5 = -2

Highlight: When solving absolute value equations, always consider both positive and negative possibilities to find all valid solutions.

Example: For 2|x + 5| = 4:

  1. Simplify to |x + 5| = 2
  2. Solve for x + 5 = 2 and x + 5 = -2
  3. Solutions are x = -3 and x = -7

Vocabulary: The term "no solution" indicates when an absolute value equation has no real number solutions that satisfy the given conditions.

J I I I I J J J J 2 e 1-6 Compound Inequalities. • 2 types of compound inequalities, or & and or and ← + -3 -2 x=-1 Dr x21 -3 -2 "1 Example

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: Compound Inequalities

This page introduces the fundamental concepts of compound inequalities and their solutions. The content focuses on two main types of compound inequalities: 'and' and 'or' operations, with detailed explanations of how to solve them.

Definition: Compound inequalities are mathematical statements that combine two or more inequalities using 'and' or 'or' operations.

Example: For the inequality -3≤x≤3, x must be greater than or equal to -3 AND less than or equal to 3.

Highlight: When solving compound inequalities with 'and', the solution must satisfy both conditions simultaneously.

The page demonstrates step-by-step solutions for various compound inequalities:

Example: Solving -3x+2>-7:

  1. Add 2 to both sides: -3x>-9
  2. Divide by -3: x<3

Vocabulary: The term "middle" refers to the value of x that must fall between two boundary points in an 'and' compound inequality.

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Learn how to solve equations with variables on both sides by simplifying expressions and evaluating equations.

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Know Solving Equations with Variables on Both Sides thumbnail

Arithmetic - Understanding Simple Interest: Calculation and Examples

Learn how simple interest works, including the formula and examples, and differentiate it from compound interest. Calculate interest earned on a savings account.

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Know Understanding Simple Interest: Calculation and Examples 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