Rovnice sú ako matematické hádanky, kde hľadáme neznáme číslo označené... Show more
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Updated Mar 13, 2026
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Jak řešit jednoduché lineární rovnice
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Úvod do riešenia rovníc a kľúčové pojmy
Rovnice ti pomôžu nájsť neznáme čísla a vyriešiť tak matematické "záhady". Predstav si to ako váhy, ktoré musíš udržať v rovnováhe.
Rovnica je matematický zápis s dvoma stranami spojenými znakom rovnosti (=), kde sa nachádza nejaká neznáma (najčastejšie x). Ľavá strana (ĽS) je všetko naľavo od znaku =, pravá strana (PS) je všetko napravo.
Koreň rovnice je to správne číslo, ktoré keď dosadíš za x, ľavá strana sa bude rovnať pravej. Ekvivalentné úpravy sú zmeny, ktoré môžeš s rovnicou robiť bez toho, aby sa zmenilo jej riešenie - ako keď pridáš na obe strany váh rovnaké závažie.
Tip: Lineárna rovnica je tá najjednoduchšia - neznáma x je v nej vždy "sama", nie je tam x² ani x³.
Ekvivalentné úpravy a postup riešenia
Tvoj cieľ je dostať neznámu x samotnú na jednu stranu a výsledok na druhú. Máš na to tri nástroje, ale vždy musíš urobiť tú istú zmenu na oboch stranách!
Pričítanie alebo odčítanie rovnakého čísla k obom stranám. Ak máš x - 3 = 7, pripočítaj k obom stranám 3 a dostaneš x = 10. Násobenie alebo delenie oboch strán rovnakým číslom (nie nulou!). Pri 2x = 10 vydeľ obe strany 2 a máš x = 5.
Postup je jednoduchý: najprv zjednoduš čo sa dá, potom presuň všetky x na jednu stranu a čísla na druhú. Keď presúvaš cez znak =, zmeň znamienko! Nakonec izoluj x delením alebo násobením.
Dôležité: Vždy si urob skúšku správnosti - dosaď výsledok do pôvodnej rovnice a skontroluj, či sa ľavá strana rovná pravej!
Riešené príklady krok za krokom
Pozrime si, ako riešiť rovnice na konkrétnych príkladoch. Každý krok si dobre zapamätaj.
Príklad 1: x + 7 = 15. Chceš sa zbaviť +7, takže od oboch strán odčítaj 7: x + 7 - 7 = 15 - 7, teda x = 8. Skúška: 8 + 7 = 15 ✓
Príklad 2: 4x - 6 = 14. Najprv pripočítaj 6: 4x = 20. Potom vydeľ 4: x = 5. Skúška: 4×5 - 6 = 20 - 6 = 14 ✓
Príklad 3: 3x + 2 = x + 10. Presuň x z pravej strany: 3x - x + 2 = 10, teda 2x + 2 = 10. Presuň číslo 2: 2x = 8. Vydeľ 2: x = 4. Skúška: 3×4 + 2 = 4 + 10, teda 14 = 14 ✓
Pamätaj si: Keď presúvaš člen cez znak =, vždy mu zmeň znamienko na opačné!
Dôležité pravidlá a tipy na záver
Zapamätaj si tieto kľúčové pravidlá, ktoré ti zabezpečia úspech pri riešení lineárnych rovníc. Sú to tvoje najlepšie pomocníky!
Vždy to isté na oboch stranách - toto je najdôležitejšie pravidlo. Čo urobíš na ľavej strane, musíš urobiť aj na pravej. Pozor na znamienka - pri presúvaní cez = sa z + stáva - a naopak. Nulou sa nedelí - nikdy!
Skúška správnosti je tvoj najlepší kamarát - vždy si prevez výsledok dosadením do pôvodnej rovnice. Najprv zjednoduš všetko, čo sa dá, potom postupuj systematicky. Môžeš si úpravy písať za lomítko, napríklad x + 5 = 10 /−5.
Povzbudenie: Riešenie rovníc je ako hra - čím viac cvičíš, tým lepší sa staneš. Každá rovnica má svoje riešenie a ty ho dokážeš nájsť!
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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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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
Jak řešit jednoduché lineární rovnice
Rovnice sú ako matematické hádanky, kde hľadáme neznáme číslo označené väčšinou písmenom x. Je to detektívna práca, ktorá ti pomôže vyriešiť množstvo problémov v matematike i v bežnom živote.
Úvod do riešenia rovníc a kľúčové pojmy
Rovnice ti pomôžu nájsť neznáme čísla a vyriešiť tak matematické "záhady". Predstav si to ako váhy, ktoré musíš udržať v rovnováhe.
Rovnica je matematický zápis s dvoma stranami spojenými znakom rovnosti (=), kde sa nachádza nejaká neznáma (najčastejšie x). Ľavá strana (ĽS) je všetko naľavo od znaku =, pravá strana (PS) je všetko napravo.
Koreň rovnice je to správne číslo, ktoré keď dosadíš za x, ľavá strana sa bude rovnať pravej. Ekvivalentné úpravy sú zmeny, ktoré môžeš s rovnicou robiť bez toho, aby sa zmenilo jej riešenie - ako keď pridáš na obe strany váh rovnaké závažie.
Tip: Lineárna rovnica je tá najjednoduchšia - neznáma x je v nej vždy "sama", nie je tam x² ani x³.
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Ekvivalentné úpravy a postup riešenia
Tvoj cieľ je dostať neznámu x samotnú na jednu stranu a výsledok na druhú. Máš na to tri nástroje, ale vždy musíš urobiť tú istú zmenu na oboch stranách!
Pričítanie alebo odčítanie rovnakého čísla k obom stranám. Ak máš x - 3 = 7, pripočítaj k obom stranám 3 a dostaneš x = 10. Násobenie alebo delenie oboch strán rovnakým číslom (nie nulou!). Pri 2x = 10 vydeľ obe strany 2 a máš x = 5.
Postup je jednoduchý: najprv zjednoduš čo sa dá, potom presuň všetky x na jednu stranu a čísla na druhú. Keď presúvaš cez znak =, zmeň znamienko! Nakonec izoluj x delením alebo násobením.
Dôležité: Vždy si urob skúšku správnosti - dosaď výsledok do pôvodnej rovnice a skontroluj, či sa ľavá strana rovná pravej!
Sign up to see the contentIt's free!
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Riešené príklady krok za krokom
Pozrime si, ako riešiť rovnice na konkrétnych príkladoch. Každý krok si dobre zapamätaj.
Príklad 1: x + 7 = 15. Chceš sa zbaviť +7, takže od oboch strán odčítaj 7: x + 7 - 7 = 15 - 7, teda x = 8. Skúška: 8 + 7 = 15 ✓
Príklad 2: 4x - 6 = 14. Najprv pripočítaj 6: 4x = 20. Potom vydeľ 4: x = 5. Skúška: 4×5 - 6 = 20 - 6 = 14 ✓
Príklad 3: 3x + 2 = x + 10. Presuň x z pravej strany: 3x - x + 2 = 10, teda 2x + 2 = 10. Presuň číslo 2: 2x = 8. Vydeľ 2: x = 4. Skúška: 3×4 + 2 = 4 + 10, teda 14 = 14 ✓
Pamätaj si: Keď presúvaš člen cez znak =, vždy mu zmeň znamienko na opačné!
Sign up to see the contentIt's free!
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Dôležité pravidlá a tipy na záver
Zapamätaj si tieto kľúčové pravidlá, ktoré ti zabezpečia úspech pri riešení lineárnych rovníc. Sú to tvoje najlepšie pomocníky!
Vždy to isté na oboch stranách - toto je najdôležitejšie pravidlo. Čo urobíš na ľavej strane, musíš urobiť aj na pravej. Pozor na znamienka - pri presúvaní cez = sa z + stáva - a naopak. Nulou sa nedelí - nikdy!
Skúška správnosti je tvoj najlepší kamarát - vždy si prevez výsledok dosadením do pôvodnej rovnice. Najprv zjednoduš všetko, čo sa dá, potom postupuj systematicky. Môžeš si úpravy písať za lomítko, napríklad x + 5 = 10 /−5.
Povzbudenie: Riešenie rovníc je ako hra - čím viac cvičíš, tým lepší sa staneš. Každá rovnica má svoje riešenie a ty ho dokážeš nájsť!
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
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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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