Inequalities are mathematical statements showing when quantities aren't equal to... Show more
Mathematics98 views·Updated May 30, 2026·2 pagesUnderstanding Inequalities
K
Karen Geronimo@karengeronimo_huhv
1
of 2
Understanding Inequalities
Inequalities are mathematical sentences that show when two quantities aren't equal to each other. They're similar to equations but instead of finding exact values, we're looking for ranges of solutions.
Inequality symbols tell us the relationship between quantities: less than (<), greater than (>), less than or equal to (≤), and greater than or equal to (≥). Each symbol has a specific meaning - for example, "≤" means "is at most" while "≥" means "is at least."
We can use inequalities in real-life situations. For instance, "A ≥ 18" could represent an age requirement, meaning someone must be at least 18 years old. Similarly, "w > 50" might represent a weight requirement for dogs, indicating the weight must be greater than 50 pounds.
💡 When graphing inequalities on a number line, use an open circle (○) for < or > (showing the endpoint isn't included) and a closed circle (●) for ≤ or ≥ (showing the endpoint is included).
2
of 2
Graphing Inequalities
Graphing inequalities on a number line helps us visualize all possible solutions. The direction of the line (left or right) shows which values satisfy the inequality. An arrow pointing right includes all greater values, while an arrow pointing left includes all lesser values.
For example, with "x ≥ -7," we place a closed circle at -7 and draw an arrow extending to the right. This shows that x can equal -7 or be any greater value. The closed circle indicates that -7 itself is part of the solution.
Combined inequalities like "2 ≤ x ≤ 9" mean x must be greater than or equal to 2 AND less than or equal to 9. On a number line, this appears as a line segment with closed circles at both endpoints.
💡 Think of inequality solutions as "regions" rather than single values. This mindset shift will help you understand why we use number lines to represent the many possible answers.
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.
Where can I download the Knowunity app?
You can download the app in the Google Play Store and in the Apple App Store.
Is Knowunity really free of charge?
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
Most popular content in Mathematics
9Most popular content
9Can't find what you're looking for? Explore other subjects.
Students love us — and so will you.
4.6/5App Store
4.7/5Google Play
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 SiOS 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 KlichAndroid 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.
AnnaiOS user
Mathematics98 views·Updated May 30, 2026·2 pagesUnderstanding Inequalities
K
Karen Geronimo@karengeronimo_huhv
Inequalities are mathematical statements showing when quantities aren't equal to each other. Unlike equations that look for exact values, inequalities help us find ranges of solutions that satisfy certain conditions. Understanding inequalities is crucial for solving many real-world problems where... Show more
1
of 2Sign up to see the content. It's free!
- Access to all documents
- Improve your grades
- Join milions of students
Understanding Inequalities
Inequalities are mathematical sentences that show when two quantities aren't equal to each other. They're similar to equations but instead of finding exact values, we're looking for ranges of solutions.
Inequality symbols tell us the relationship between quantities: less than (<), greater than (>), less than or equal to (≤), and greater than or equal to (≥). Each symbol has a specific meaning - for example, "≤" means "is at most" while "≥" means "is at least."
We can use inequalities in real-life situations. For instance, "A ≥ 18" could represent an age requirement, meaning someone must be at least 18 years old. Similarly, "w > 50" might represent a weight requirement for dogs, indicating the weight must be greater than 50 pounds.
💡 When graphing inequalities on a number line, use an open circle (○) for < or > (showing the endpoint isn't included) and a closed circle (●) for ≤ or ≥ (showing the endpoint is included).
2
of 2Sign up to see the content. It's free!
- Access to all documents
- Improve your grades
- Join milions of students
Graphing Inequalities
Graphing inequalities on a number line helps us visualize all possible solutions. The direction of the line (left or right) shows which values satisfy the inequality. An arrow pointing right includes all greater values, while an arrow pointing left includes all lesser values.
For example, with "x ≥ -7," we place a closed circle at -7 and draw an arrow extending to the right. This shows that x can equal -7 or be any greater value. The closed circle indicates that -7 itself is part of the solution.
Combined inequalities like "2 ≤ x ≤ 9" mean x must be greater than or equal to 2 AND less than or equal to 9. On a number line, this appears as a line segment with closed circles at both endpoints.
💡 Think of inequality solutions as "regions" rather than single values. This mindset shift will help you understand why we use number lines to represent the many possible answers.
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.
Where can I download the Knowunity app?
You can download the app in the Google Play Store and in the Apple App Store.
Is Knowunity really free of charge?
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
Most popular content in Mathematics
9Most popular content
9Can't find what you're looking for? Explore other subjects.
Students love us — and so will you.
4.6/5App Store
4.7/5Google Play
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 SiOS 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 KlichAndroid 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.
AnnaiOS user