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Maths
5 Dec 2025
343
2 pages
Poppy @p.wl
Inequalities might seem tricky at first, but they're actually just like equations with a twist - instead of... Show more
Think of inequalities as mathematical statements that compare two things that aren't equal. You'll use four main symbols < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to).
When drawing inequalities on a number line, remember this simple rule open circles for strict inequalities (< or >) and closed circles when the number itself is included (≤ or ≥). This visual approach makes it much easier to see what values work.
Solving inequalities works exactly like solving equations - use inverse operations to isolate the variable. The key difference is that your answer will be a range rather than a single number. For example, if you get m ≥ -2, this means m can be any number from -2 upwards.
Quick Tip When finding integer solutions, list all the whole numbers (including negatives and zero) that fit within your inequality range.
Set notation gives you a posh way to write inequality solutions using curly brackets. The expression {x x ≥ 5} reads as "the set of all x values such that x is greater than or equal to 5" - it's just a formal way of expressing the same idea.
Compound inequalities like 1 ≤ 2x + 3 < 15 need splitting into two separate parts. Solve each part independently, then combine your answers to find the overlapping range.
Quadratic inequalities bring graphs into the mix. When you see x² + 2x - 8 ≤ 0, factorise it first, then think about where the parabola sits above or below the x-axis. Values below the x-axis (≤ 0) give you one continuous range, whilst values above (≥ 0) often give you two separate ranges.
Remember For quadratic inequalities, sketching a quick graph helps you visualise which parts of the parabola satisfy your inequality.
Our AI Companion is a student-focused AI tool that offers more than just answers. Built on millions of Knowunity resources, it provides relevant information, personalised study plans, quizzes, and content directly in the chat, adapting to your individual learning journey.
You can download the app from Google Play Store and Apple App Store.
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
9
Smart Tools NEW
Transform this note into: ✓ 50+ Practice Questions ✓ Interactive Flashcards ✓ Full Mock Exam ✓ Essay Outlines
Explore the fundamentals of quadratic inequalities, including how to solve them and identify solution sets. This summary covers key concepts such as multi-step inequalities, integer solutions, and graphical representations. Ideal for students looking to master the topic for exams or homework.
MathsExplore the fundamentals of solving inequalities, including one-step, two-step, and multi-step inequalities. Learn the key rules, such as reversing the inequality sign when dividing by a negative number. This summary provides essential insights for mastering inequality equations.
MathsExplore the fundamentals of inequalities, including one-step, two-step, and multi-step solutions. Learn how to graph inequalities and understand compound inequalities with clear examples and step-by-step explanations. Ideal for students preparing for exams or seeking to strengthen their math skills.
MathsQuotes from every main character
English LiteratureApp Store
Google 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 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
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
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
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
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 apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
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
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
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
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
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 apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
Poppy
@p.wl
Inequalities might seem tricky at first, but they're actually just like equations with a twist - instead of finding one exact answer, you're finding a range of possible values. Once you master the symbols and rules, you'll be solving inequality... Show more
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Think of inequalities as mathematical statements that compare two things that aren't equal. You'll use four main symbols: < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to).
When drawing inequalities on a number line, remember this simple rule: open circles for strict inequalities (< or >) and closed circles when the number itself is included (≤ or ≥). This visual approach makes it much easier to see what values work.
Solving inequalities works exactly like solving equations - use inverse operations to isolate the variable. The key difference is that your answer will be a range rather than a single number. For example, if you get m ≥ -2, this means m can be any number from -2 upwards.
Quick Tip: When finding integer solutions, list all the whole numbers (including negatives and zero) that fit within your inequality range.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Set notation gives you a posh way to write inequality solutions using curly brackets. The expression {x : x ≥ 5} reads as "the set of all x values such that x is greater than or equal to 5" - it's just a formal way of expressing the same idea.
Compound inequalities like 1 ≤ 2x + 3 < 15 need splitting into two separate parts. Solve each part independently, then combine your answers to find the overlapping range.
Quadratic inequalities bring graphs into the mix. When you see x² + 2x - 8 ≤ 0, factorise it first, then think about where the parabola sits above or below the x-axis. Values below the x-axis (≤ 0) give you one continuous range, whilst values above (≥ 0) often give you two separate ranges.
Remember: For quadratic inequalities, sketching a quick graph helps you visualise which parts of the parabola satisfy your inequality.
Our AI Companion is a student-focused AI tool that offers more than just answers. Built on millions of Knowunity resources, it provides relevant information, personalised study plans, quizzes, and content directly in the chat, adapting to your individual learning journey.
You can download the app from Google Play Store and Apple App Store.
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
9
Smart Tools NEW
Transform this note into: ✓ 50+ Practice Questions ✓ Interactive Flashcards ✓ Full Mock Exam ✓ Essay Outlines
Explore the fundamentals of quadratic inequalities, including how to solve them and identify solution sets. This summary covers key concepts such as multi-step inequalities, integer solutions, and graphical representations. Ideal for students looking to master the topic for exams or homework.
MathsExplore the fundamentals of solving inequalities, including one-step, two-step, and multi-step inequalities. Learn the key rules, such as reversing the inequality sign when dividing by a negative number. This summary provides essential insights for mastering inequality equations.
MathsExplore the fundamentals of inequalities, including one-step, two-step, and multi-step solutions. Learn how to graph inequalities and understand compound inequalities with clear examples and step-by-step explanations. Ideal for students preparing for exams or seeking to strengthen their math skills.
MathsQuotes from every main character
English LiteratureApp Store
Google 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 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
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
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
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
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 apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
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
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
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
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
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 apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
Sociology