Solving equations is like being a detective - you're hunting... Show more
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Updated Mar 15, 2026
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Mastering Linear Equations: Solve Like a Pro
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What's All This About?
Solving equations means finding the value of an unknown number, called a variable. Your main mission is simple: get that variable all by itself on one side of the equals sign.
An equation is just a maths sentence saying two things are equal - it always has that equals sign in the middle. The variable is the mystery letter (like x or y) you need to find, while constants are just regular numbers hanging about.
Here's your secret weapon: inverse operations. These are opposite operations that undo each other - addition undoes subtraction, multiplication undoes division, and so on.
Remember: Addition ↔ Subtraction and Multiplication ↔ Division are perfect pairs!
Cracking One-Step Equations
These are the easiest equations because they only need one inverse operation to solve. You've basically got two types to deal with.
For addition and subtraction equations, spot what number is being added or subtracted from your variable. Then do the opposite to both sides. If you see x + 6 = 14, subtract 6 from both sides to get x = 8.
For multiplication and division equations, look at what number your variable is being multiplied or divided by. Then do the reverse to both sides. If you have 4y = 20, divide both sides by 4 to get y = 5.
Top Tip: Always do the same operation to both sides - this keeps your equation balanced like a perfect seesaw!
Tackling Two-Step Equations
Two-step equations need two moves to solve, and here's the clever bit - you work backwards through BIDMAS. Think of it like unwrapping a present where you undo the last thing that was done first.
Step 1: Deal with any addition or subtraction first. Get rid of the constant (the number on its own) by doing the opposite operation to both sides.
Step 2: Then handle any multiplication or division. Work on the number attached to your variable by using its inverse operation.
For example, with 2x + 5 = 15, first subtract 5 from both sides , then divide both sides by 2 .
Golden Rule: Always tackle the lone number first, then deal with whatever's attached to your variable!
Working Through Real Examples
Let's see how this works with proper exam-style examples. For a simple equation like a - 9 = 11, you add 9 to both sides to get a = 20.
With two-step equations like 3m + 4 = 19, first subtract 4 from both sides , then divide both sides by 3 . Easy when you know the steps!
Even trickier ones like k/5 - 2 = 3 follow the same pattern. Add 2 to both sides first , then multiply both sides by 5 .
Always check your answer by popping it back into the original equation. It takes seconds and can save you marks in a test!
Pro Move: Checking your answer is like having a safety net - it catches mistakes before they cost you points!
Key Things to Remember
The golden rule of algebra is sacred: whatever you do to one side, you absolutely must do to the other. No exceptions, ever!
Watch out for negative numbers - if you have -3x = 12, you divide by -3 (not just 3) to get x = -4. Also remember that x on its own is really 1x, and x/2 just means x ÷ 2.
For two-step equations, your order of attack is: undo addition or subtraction first, then tackle multiplication or division. Keep everything balanced and always check your final answer.
Test Strategy: Goal → Get the variable alone. Method → Use inverse operations. Rule → Do the same to both sides. Check → Put your answer back in!
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
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
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
Mastering Linear Equations: Solve Like a Pro
Solving equations is like being a detective - you're hunting for the mystery value of a variable (usually x or y). Think of an equation as a perfectly balanced weighing scale, where whatever you do to one side, you must... Show more
What's All This About?
Solving equations means finding the value of an unknown number, called a variable. Your main mission is simple: get that variable all by itself on one side of the equals sign.
An equation is just a maths sentence saying two things are equal - it always has that equals sign in the middle. The variable is the mystery letter (like x or y) you need to find, while constants are just regular numbers hanging about.
Here's your secret weapon: inverse operations. These are opposite operations that undo each other - addition undoes subtraction, multiplication undoes division, and so on.
Remember: Addition ↔ Subtraction and Multiplication ↔ Division are perfect pairs!
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Cracking One-Step Equations
These are the easiest equations because they only need one inverse operation to solve. You've basically got two types to deal with.
For addition and subtraction equations, spot what number is being added or subtracted from your variable. Then do the opposite to both sides. If you see x + 6 = 14, subtract 6 from both sides to get x = 8.
For multiplication and division equations, look at what number your variable is being multiplied or divided by. Then do the reverse to both sides. If you have 4y = 20, divide both sides by 4 to get y = 5.
Top Tip: Always do the same operation to both sides - this keeps your equation balanced like a perfect seesaw!
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Tackling Two-Step Equations
Two-step equations need two moves to solve, and here's the clever bit - you work backwards through BIDMAS. Think of it like unwrapping a present where you undo the last thing that was done first.
Step 1: Deal with any addition or subtraction first. Get rid of the constant (the number on its own) by doing the opposite operation to both sides.
Step 2: Then handle any multiplication or division. Work on the number attached to your variable by using its inverse operation.
For example, with 2x + 5 = 15, first subtract 5 from both sides , then divide both sides by 2 .
Golden Rule: Always tackle the lone number first, then deal with whatever's attached to your variable!
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Working Through Real Examples
Let's see how this works with proper exam-style examples. For a simple equation like a - 9 = 11, you add 9 to both sides to get a = 20.
With two-step equations like 3m + 4 = 19, first subtract 4 from both sides , then divide both sides by 3 . Easy when you know the steps!
Even trickier ones like k/5 - 2 = 3 follow the same pattern. Add 2 to both sides first , then multiply both sides by 5 .
Always check your answer by popping it back into the original equation. It takes seconds and can save you marks in a test!
Pro Move: Checking your answer is like having a safety net - it catches mistakes before they cost you points!
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Key Things to Remember
The golden rule of algebra is sacred: whatever you do to one side, you absolutely must do to the other. No exceptions, ever!
Watch out for negative numbers - if you have -3x = 12, you divide by -3 (not just 3) to get x = -4. Also remember that x on its own is really 1x, and x/2 just means x ÷ 2.
For two-step equations, your order of attack is: undo addition or subtraction first, then tackle multiplication or division. Keep everything balanced and always check your final answer.
Test Strategy: Goal → Get the variable alone. Method → Use inverse operations. Rule → Do the same to both sides. Check → Put your answer back in!
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.
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Most popular content in Mathematics
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
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