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Fun with Inequalities: Solving with Multiplication, Division, Addition, and Subtraction!

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Michelle

7/7/2023

Arithmetic

Pre-Algebra: Graphing and Solving Inequalities

Fun with Inequalities: Solving with Multiplication, Division, Addition, and Subtraction!

This transcript covers solving inequalities, including graphing, one-step, and two-step inequalities. It explains inequality symbols, graphing techniques, and rules for solving inequalities with different operations.

• The document introduces inequality symbols and their meanings.
• It covers graphing inequalities on a number line, using open and closed circles.
• One-step inequalities involving addition, subtraction, multiplication, and division are explained.
• The concept of flipping inequality signs when multiplying or dividing by negative numbers is emphasized.
• Two-step inequalities and their solving process are demonstrated.

...

7/7/2023

140

C
Graphing and solving Inequalities
symbol
>
<
ex:
2
S
-4-3-2
-3 -2
Name
greater than
less than
greater than
or equal to
less than or
equal

View

Two-Step Inequalities

This page focuses on solving two-step inequalities, which are more complex than one-step inequalities and require multiple operations to solve. It provides a step-by-step approach to solving these types of problems, which is crucial for students learning about solving inequalities by multiplication and division.

The page begins with two examples of two-step inequalities:

  1. 4x + 1 ≤ 13
  2. -3x + 2 > 11

For each example, the solving process is broken down into clear steps:

Example: Solving 4x + 1 ≤ 13 Step 1: Subtract 1 from both sides: 4x ≤ 12 Step 2: Divide both sides by 4: x ≤ 3

Example: Solving -3x + 2 > 11 Step 1: Subtract 2 from both sides: -3x > 9 Step 2: Divide both sides by -3 andfliptheinequalitysignand flip the inequality sign: x < -3

The document emphasizes the order of operations when solving two-step inequalities:

Highlight: Always perform addition or subtraction first, followed by multiplication or division.

It also reiterates the important rule about flipping the inequality sign when dividing by a negative number, which is a key concept in solving inequalities using multiplication and division.

The page concludes with graphing the solutions of these two-step inequalities on a number line, reinforcing the concepts of open and closed circles introduced on the previous page.

This comprehensive approach to solving and graphing two-step inequalities provides students with a solid foundation for understanding more complex inequality problems and prepares them for advanced topics in algebra.

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Arithmetic

140

Jul 7, 2023

2 pages

Fun with Inequalities: Solving with Multiplication, Division, Addition, and Subtraction!

This transcript covers solving inequalities, including graphing, one-step, and two-step inequalities. It explains inequality symbols, graphing techniques, and rules for solving inequalities with different operations.

• The document introduces inequality symbols and their meanings.
• It covers graphing inequalities on... Show more

C
Graphing and solving Inequalities
symbol
>
<
ex:
2
S
-4-3-2
-3 -2
Name
greater than
less than
greater than
or equal to
less than or
equal

Sign up to see the contentIt's free!

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Two-Step Inequalities

This page focuses on solving two-step inequalities, which are more complex than one-step inequalities and require multiple operations to solve. It provides a step-by-step approach to solving these types of problems, which is crucial for students learning about solving inequalities by multiplication and division.

The page begins with two examples of two-step inequalities:

  1. 4x + 1 ≤ 13
  2. -3x + 2 > 11

For each example, the solving process is broken down into clear steps:

Example: Solving 4x + 1 ≤ 13 Step 1: Subtract 1 from both sides: 4x ≤ 12 Step 2: Divide both sides by 4: x ≤ 3

Example: Solving -3x + 2 > 11 Step 1: Subtract 2 from both sides: -3x > 9 Step 2: Divide both sides by -3 andfliptheinequalitysignand flip the inequality sign: x < -3

The document emphasizes the order of operations when solving two-step inequalities:

Highlight: Always perform addition or subtraction first, followed by multiplication or division.

It also reiterates the important rule about flipping the inequality sign when dividing by a negative number, which is a key concept in solving inequalities using multiplication and division.

The page concludes with graphing the solutions of these two-step inequalities on a number line, reinforcing the concepts of open and closed circles introduced on the previous page.

This comprehensive approach to solving and graphing two-step inequalities provides students with a solid foundation for understanding more complex inequality problems and prepares them for advanced topics in algebra.

C
Graphing and solving Inequalities
symbol
>
<
ex:
2
S
-4-3-2
-3 -2
Name
greater than
less than
greater than
or equal to
less than or
equal

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Graphing and Solving Inequalities

This page introduces the fundamental concepts of inequalities, their symbols, and how to graph them on a number line. It covers essential information for students learning to solve inequalities with multiplication and division.

The page begins by presenting the four main inequality symbols:

  • Greater than >>
  • Less than <<
  • Greater than or equal to
  • Less than or equal to

Vocabulary: Inequality symbols are mathematical symbols used to show the relationship between two expressions that are not equal.

The document then explains how to graph inequalities on a number line, emphasizing the difference between open and closed circles:

Highlight: Open circles are used for strict inequalities >or<> or <, while closed circles represent inequalities that include equality or≥ or ≤.

Several examples of graphing inequalities are provided, such as x > 0 and x > -2, to illustrate the correct use of open and closed circles on a number line.

The page then delves into solving one-step inequalities, covering addition, subtraction, multiplication, and division. It emphasizes a crucial rule when solving inequalities:

Definition: When multiplying or dividing an inequality by a negative number, the inequality sign must be flipped.

This rule is particularly important for solving inequalities using multiplication and division. The document provides examples to demonstrate this concept, such as:

Example: -7x > 63 Dividing both sides by -7 anegativenumbera negative number, we flip the sign: x < -9

The page concludes with a note on solving inequalities with addition and subtraction, stating that the inequality sign does not change in these operations unless adding a negative number, which is equivalent to subtraction.

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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

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