Graphing inequalities is all about showing solutions on a number... Show more
Mathematics35 views·Updated May 29, 2026·2 pagesGraphing Inequalities: Math 7 Study Notes
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Understanding Inequalities
An inequality is a math statement that compares expressions using symbols like < (less than) or ≥ (greater than or equal to). Unlike equations, inequalities give you a range of solutions.
When you graph inequalities, you use open circles for < and > symbols (not including the number), and closed circles for ≤ and ≥ symbols (including the number). Then you draw an arrow showing all the solutions.
For example, if Mr. Perry is over 147 years old, we write P > 147 and draw an open circle at 147 with an arrow pointing right. If he's at least 20, we write P ≥ 20 and draw a closed circle at 20 with an arrow pointing right.
Remember this! When you multiply or divide both sides of an inequality by a negative number, you must flip the inequality symbol. For example, if -4x > 20, then x < -5 after dividing by -4.
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Solving Inequalities
To solve inequalities, isolate the variable just like you would in an equation. You can add, subtract, multiply, or divide both sides by the same number.
For example, to solve x/2 < -10, multiply both sides by 2 to get x < -20. For problems like x/-3 < -15, multiply both sides by -3 (and flip the sign!) to get x > 45.
When describing real-world situations, use clear inequality symbols. If Mr. Perry has no more than $3 in his wallet, we write x ≤ 3, showing he has $3 or less.
Quick tip: Drawing a few test points on a number line can help you check if you've solved the inequality correctly. Try values on both sides of your solution point to confirm!
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Mathematics35 views·Updated May 29, 2026·2 pagesGraphing Inequalities: Math 7 Study Notes
Graphing inequalities is all about showing solutions on a number line. You'll learn how to use symbols like < and ≤ to show relationships between numbers, and how to solve and graph these statements visually.
1
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Understanding Inequalities
An inequality is a math statement that compares expressions using symbols like < (less than) or ≥ (greater than or equal to). Unlike equations, inequalities give you a range of solutions.
When you graph inequalities, you use open circles for < and > symbols (not including the number), and closed circles for ≤ and ≥ symbols (including the number). Then you draw an arrow showing all the solutions.
For example, if Mr. Perry is over 147 years old, we write P > 147 and draw an open circle at 147 with an arrow pointing right. If he's at least 20, we write P ≥ 20 and draw a closed circle at 20 with an arrow pointing right.
Remember this! When you multiply or divide both sides of an inequality by a negative number, you must flip the inequality symbol. For example, if -4x > 20, then x < -5 after dividing by -4.
2
of 2Sign up to see the content. It's free!
- Access to all documents
- Improve your grades
- Join milions of students
Solving Inequalities
To solve inequalities, isolate the variable just like you would in an equation. You can add, subtract, multiply, or divide both sides by the same number.
For example, to solve x/2 < -10, multiply both sides by 2 to get x < -20. For problems like x/-3 < -15, multiply both sides by -3 (and flip the sign!) to get x > 45.
When describing real-world situations, use clear inequality symbols. If Mr. Perry has no more than $3 in his wallet, we write x ≤ 3, showing he has $3 or less.
Quick tip: Drawing a few test points on a number line can help you check if you've solved the inequality correctly. Try values on both sides of your solution point to confirm!
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.
Similar Content
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