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Easy Steps for Solving Compound Inequalities and Absolute Value Problems

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Clara Vandenbelt

10/23/2023

Arithmetic

Solving Compound Inequalities and Absolute Value Equations

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Arithmetic

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Systems of Equations

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Intro to Systems of Equations

Easy Steps for Solving Compound Inequalities and Absolute Value Problems

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

69

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.

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Subjects

Arithmetic

Systems of Equations

Intro to Systems of Equations

 

Arithmetic

•

69

•

Oct 23, 2023

•

2 pages

Easy Steps for Solving Compound Inequalities and Absolute Value Problems

user profile picture

Clara Vandenbelt

@clara_tiara0

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... Show more

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

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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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Paul T

iOS user

The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.

Stefan S

iOS user

This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.

Samantha Klich

Android user

Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.

Anna

iOS user

I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️

Thomas R

iOS user

Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades

Brad T

Android user

Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍

David K

iOS user

The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!

Sudenaz Ocak

Android user

In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.

Greenlight Bonnie

Android user

I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend

Aubrey

iOS user

Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀

Marco B

iOS user

THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮

Elisha

iOS user

This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!

Paul T

iOS user