•

Updated Apr 15, 2026

•

1 page

How to Graph Linear Inequalities Step by Step - Easy for Kids!

Vivian Quach

@vivianquach_wzmx

Linear inequalities are mathematical expressions that involve variables and inequality... Show more

# solving linear inequalities

- A linear inequality is similar to a linear equation, but
the equal sign is replaced with an inequality symb

Solving and Graphing Linear Inequalities

Linear inequalities are mathematical expressions similar to linear equations, but they use inequality symbols instead of an equal sign. This page covers how to identify solutions and graph linear inequalities.

Identifying Solutions

A solution to a linear inequality is any ordered pair that makes the inequality true. To determine if an ordered pair is a solution, substitute the values into the inequality and check if it holds true.

Example: For the inequality y < x - 1, we can check if (7, 3) is a solution: 3 < 7 - 1 3 < 6 This is true, so (7, 3) is a solution.

Example: For the inequality y > 3x + 2, we can check if (4, 5) is a solution: 5 > 3(4) + 2 5 > 14 This is false, so (4, 5) is not a solution.

Graphing Inequalities

When graphing linear inequalities, the type of line and shading used depends on the inequality symbol:

Highlight:

For y ≤ or y ≥, use a solid line.

For y < or y >, use a dashed line.

For > or ≥, shade above the line.

For < or ≤, shade below the line.

Vocabulary:

Solid line: A continuous, unbroken line used for inequalities that include the boundary (≤ or ≥).

Dashed line: A line made up of short, disconnected segments used for strict inequalities (< or >).

Understanding these rules is crucial for graphing linear inequalities step by step. When using a graphing linear inequalities calculator, it's important to input the inequality correctly to ensure accurate shading and line type.

Definition: A system of linear inequalities consists of two or more linear inequalities that must be satisfied simultaneously. The solution is the region where all inequalities are true.

Practicing with a graphing linear inequalities worksheet can help reinforce these concepts and improve your skills in solving linear inequalities with two variables. Remember, the solution of an inequality is not just a single point, but an entire region on the coordinate plane that satisfies the given conditions.

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 Algebra 1

7th Grade Math

Algebra 1 and all of the other stuff

Algebra 1

7th

Mastering Algebra 1: Essential Flashcards

Learn key concepts of Algebra 1 with these flashcards. Explore slope-intercept form, properties, equations, and expressions. Boost your math skills and ace your exams!

Algebra 1

8th

wizards

Mathematics is the most loved and also the most feared subjects by students across the world. Have you been worrying about your upcoming math test? Practice these 30 maths quiz questions to ensure you are at the top of your game!

Algebra 1

Interior and exterior angle measures

Interior and exterior angle measures practice

Algebra 1

9th

Expressions and Operations

Algebra 1 - unit 1 - covers: integer rules, order of operations, evaluating algerbraic expressions, simplifying algebraic expressions, and translating expressions.

Algebra 1

9th

Order of Operations and the Distributive property

PEMDAS and distributing

Algebra 1

Algebraic expressions

A number means an unknown quantity.

Algebra 1

Combining like terms in expressions.

Learn how to identify and combine like terms in algebraic expressions to simplify equations.

Algebra 1

9th

Integer Rules

A review of Integer concepts and how to solve integers

Algebra 1

Can't find what you're looking for? Explore other subjects.

Students love us — and so will you.

4.6/5

App Store

4.7/5

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

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 Knowunity AI. 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

Stefan S

iOS user

Samantha Klich

Android user

Anna

iOS user

Thomas R

iOS user

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

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

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

Elisha

iOS user

Paul T

iOS user

Algebra 1

•

845

•

Updated Apr 15, 2026

•

1 page

How to Graph Linear Inequalities Step by Step - Easy for Kids!

Vivian Quach

@vivianquach_wzmx

Linear inequalities are mathematical expressions that involve variables and inequality symbols. They are used to represent relationships between quantities that are not exactly equal. This guide explains how to solve and graph linear inequalities, providing step-by-step instructions and examples.

• ... Show more

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

Solving and Graphing Linear Inequalities

Identifying Solutions

Example: For the inequality y < x - 1, we can check if (7, 3) is a solution: 3 < 7 - 1 3 < 6 This is true, so (7, 3) is a solution.

Example: For the inequality y > 3x + 2, we can check if (4, 5) is a solution: 5 > 3(4) + 2 5 > 14 This is false, so (4, 5) is not a solution.

Graphing Inequalities

When graphing linear inequalities, the type of line and shading used depends on the inequality symbol:

Highlight:

For y ≤ or y ≥, use a solid line.

For y < or y >, use a dashed line.

For > or ≥, shade above the line.

For < or ≤, shade below the line.

Vocabulary:

Solid line: A continuous, unbroken line used for inequalities that include the boundary (≤ or ≥).

Dashed line: A line made up of short, disconnected segments used for strict inequalities (< or >).

Definition: A system of linear inequalities consists of two or more linear inequalities that must be satisfied simultaneously. The solution is the region where all inequalities are true.