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Dali Guevara
12/2/2025
Pre-algebra
Algebra 8 grado
112
•
Dec 2, 2025
•
Dali Guevara
@daliguevara
Welcome to 8th-grade algebra! These notes cover the essential concepts... Show more
An expression is a combination of numbers, variables, and operations that represents a value. When you need to simplify expressions, combine like terms and follow the order of operations (PEMDAS).
Equations show that two expressions are equal to each other. To solve them, isolate the variable on one side by applying inverse operations to both sides. Remember, whatever you do to one side of the equation, you must do to the other side to maintain equality.
When evaluating an expression, substitute specific values for the variables and simplify following the order of operations. This skill is essential for checking your work and solving word problems.
Pro Tip: Think of solving equations like balancing a scale - whatever you do to one side, you must do to the other to keep things balanced!
Inequalities show relationships between expressions using symbols like < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to). Solve them similar to equations, but remember to flip the inequality sign when multiplying or dividing by a negative number.
Linear functions create straight lines when graphed. The equation form y = mx + b shows two important parts: the slope (m) tells how steep the line is, and the y-intercept (b) shows where the line crosses the y-axis.
Understanding linear functions helps you model real-world relationships like distance over time or cost versus quantity. You'll use these concepts constantly in future math classes!
Remember: When you multiply or divide an inequality by a negative number, you must reverse the inequality symbol (< becomes > and vice versa).
A system of equations contains two or more equations with common solutions. You can solve these systems by graphing (finding where lines intersect), substitution (replacing variables), or elimination (combining equations to cancel variables).
Exponents represent repeated multiplication. For example, a² means a multiplied by itself. Negative exponents indicate reciprocals - a⁻³ equals 1/a³. This concept becomes very useful when working with fractions and decimals.
Scientific notation helps express very large or very small numbers using powers of 10. For instance, 4,500,000 becomes 4.5 × 10⁶. This notation is especially helpful in science classes when working with extremely large or small measurements.
Quick Tip: When solving systems by graphing, the solution is the point where the lines intersect. If they never intersect, the system has no solution!
A polynomial is an expression with one or more terms, where each term has a coefficient and a variable raised to a power. You can add, subtract, multiply, and divide polynomials using specific techniques for each operation.
Like terms have the same variables raised to the same powers . You can combine them by adding or subtracting their coefficients.
The order of operations (PEMDAS) reminds you to solve math problems in this sequence: Parentheses, Exponents, Multiplication and Division (left to right), then Addition and Subtraction (left to right).
Inverse operations undo each other, like addition/subtraction or multiplication/division. When solving equations, you'll use these pairs to isolate variables.
Challenge Yourself: Try factoring polynomials to break them into simpler expressions. This skill will be crucial when you study quadratic equations next year!
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.
You can download the app in the Google Play Store and in the Apple App Store.
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
App 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
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
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
Dali Guevara
@daliguevara
Welcome to 8th-grade algebra! These notes cover the essential concepts you'll need to master this year. From working with expressions to solving equations and graphing functions, these core skills will help you build a strong foundation for more advanced math.
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Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
An expression is a combination of numbers, variables, and operations that represents a value. When you need to simplify expressions, combine like terms and follow the order of operations (PEMDAS).
Equations show that two expressions are equal to each other. To solve them, isolate the variable on one side by applying inverse operations to both sides. Remember, whatever you do to one side of the equation, you must do to the other side to maintain equality.
When evaluating an expression, substitute specific values for the variables and simplify following the order of operations. This skill is essential for checking your work and solving word problems.
Pro Tip: Think of solving equations like balancing a scale - whatever you do to one side, you must do to the other to keep things balanced!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Inequalities show relationships between expressions using symbols like < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to). Solve them similar to equations, but remember to flip the inequality sign when multiplying or dividing by a negative number.
Linear functions create straight lines when graphed. The equation form y = mx + b shows two important parts: the slope (m) tells how steep the line is, and the y-intercept (b) shows where the line crosses the y-axis.
Understanding linear functions helps you model real-world relationships like distance over time or cost versus quantity. You'll use these concepts constantly in future math classes!
Remember: When you multiply or divide an inequality by a negative number, you must reverse the inequality symbol (< becomes > and vice versa).
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
A system of equations contains two or more equations with common solutions. You can solve these systems by graphing (finding where lines intersect), substitution (replacing variables), or elimination (combining equations to cancel variables).
Exponents represent repeated multiplication. For example, a² means a multiplied by itself. Negative exponents indicate reciprocals - a⁻³ equals 1/a³. This concept becomes very useful when working with fractions and decimals.
Scientific notation helps express very large or very small numbers using powers of 10. For instance, 4,500,000 becomes 4.5 × 10⁶. This notation is especially helpful in science classes when working with extremely large or small measurements.
Quick Tip: When solving systems by graphing, the solution is the point where the lines intersect. If they never intersect, the system has no solution!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
A polynomial is an expression with one or more terms, where each term has a coefficient and a variable raised to a power. You can add, subtract, multiply, and divide polynomials using specific techniques for each operation.
Like terms have the same variables raised to the same powers . You can combine them by adding or subtracting their coefficients.
The order of operations (PEMDAS) reminds you to solve math problems in this sequence: Parentheses, Exponents, Multiplication and Division (left to right), then Addition and Subtraction (left to right).
Inverse operations undo each other, like addition/subtraction or multiplication/division. When solving equations, you'll use these pairs to isolate variables.
Challenge Yourself: Try factoring polynomials to break them into simpler expressions. This skill will be crucial when you study quadratic equations next year!
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.
You can download the app in the Google Play Store and in the Apple App Store.
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
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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
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
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