Slovné úlohy ťa strašia? Neboj sa! Vlastne sú to len... Show more
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Updated Mar 21, 2026
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Riešenie Slovných Úloh Pomocou Lineárnych Rovníc
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Čo sú slovné úlohy a prečo sú dôležité
Predstav si, že matematika je ako prekladateľ - pomáha ti riešiť skutočné problémy zo života. Slovné úlohy sú presne takéto príbehy napísané slovami, ktoré musíš "preložiť" do matematického jazyka.
Väčšina týchto úloh ťa dovedie k lineárnej rovnici - to je rovnica, kde neznáma (zvyčajne x) nie je umocnená. Vyzerá napríklad takto: 2x + 5 = 11.
Kľúčové pojmy, ktoré musíš poznať: neznáma je to, čo hľadáš (označuje sa písmenom), riešenie rovnice je hodnota, ktorá rovnicu "vybalansuje", a skúška správnosti je overenie, či tvoj výsledok naozaj sedí.
💡 Tip: Na písomke určite budú, takže sa oplatí to pochopiť!
Postup riešenia krok za krokom
Riešenie slovných úloh má jasné pravidlá. Keď ich budeš dodržiavať, nemôžeš sa pokaziť!
Najprv si úlohu poriadne prečítaj - aj dvakrát, ak treba. Zisti, čo už vieš (dané) a čo máš zistiť (hľadané). Potom si zvol neznámu - rozhodni, čo bude tvoje x a zapíš si to!
Ďalej vyjadri všetky údaje pomocou neznámej. Toto býva najťažší krok - musíš správne preložiť slová do matematiky. Napríklad "Janko má o 5 eur viac ako Marienka" znamená, že ak Marienka má x eur, Janko má x + 5 eur.
Nakonec zostav rovnicu - nájdi v úlohe nejakú rovnosť alebo vzťah. Ak "spolu majú 48 rokov", sčítaš ich veky a dáš to rovné 48.
💡 Pozor: "O 5 viac" = sčítanie, "trikrát viac" = násobenie!
Dokončenie riešenia a skúška
Po zostavení rovnice ju vyrieš štandardnými postupmi - prenášaš členy cez rovnítko a dbáš na znamienka. Toto už zvládneš!
Skúška správnosti je kľúčová! Nedosadzuj len do rovnice, ale vráť sa k pôvodnej slovnej úlohe. Ak ti vyšlo, že syn má 12 rokov a otec 36, over si: je otec trikrát starší? (3 × 12 = 36 ✓) Majú spolu 48 rokov? (12 + 36 = 48 ✓)
Odpoveď musí byť slovná a musí odpovedať na otázku z úlohy. Nezabudni na jednotky! Nestačí napísať "x = 12", ale "Syn má 12 rokov a otec má 36 rokov."
Skontroluj si aj realitu výsledku - môže byť počet ľudí záporný? Určite nie! Ak ti vyjde niečo čudné, niekde je chyba.
💡 Dôležité: Vždy si zapíš, čo tvoje x predstavuje - bez toho sa ľahko stratíš!
Riešený príklad: Súčet čísel po sebe
Skúsme si to na konkrétnom príklade! Úloha: Súčet troch po sebe idúcich prirodzených čísel je 63. Ktoré sú to čísla?
Môj postup: Prvé číslo označím ako x, druhé bude x + 1, tretie x + 2. Ich súčet je 63, takže: x + + = 63.
Riešenie rovnice: x + x + 1 + x + 2 = 63, čiže 3x + 3 = 63. Po úprave 3x = 60, takže x = 20. Hľadané čísla sú teda 20, 21, 22.
Skúška: 20 + 21 + 22 = 63 ✓ a sú to po sebe idúce čísla ✓. Odpoveď: Hľadané čísla sú 20, 21 a 22.
💡 Tip: Pri po sebe idúcich číslach si ušetríš prácu, keď prvé označíš ako x!
Ďalšie riešené príklady
Príklad s vekom: Otec je trikrát starší ako syn. Spolu majú 48 rokov. Koľko má kto rokov?
Syn má x rokov, otec má 3x rokov. Spolu: x + 3x = 48, čiže 4x = 48, takže x = 12. Odpoveď: Syn má 12 rokov, otec 36 rokov.
Príklad so žiakmi: V triede je 28 žiakov. Chlapcov je o 4 viac ako dievčat. Koľko je chlapcov a dievčat?
Dievčat je x, chlapcov x + 4. Spolu: x + = 28, čiže 2x + 4 = 28, takže 2x = 24 a x = 12. Odpoveď: 12 dievčat a 16 chlapcov.
Vidíš? Keď poznáš postup, lineárne rovnice z týchto úloh sa riešia úplne štandardne!
💡 Skúška vždy: 12 + 16 = 28 ✓, 16 - 12 = 4 ✓
Dôležité tipy a záver
Pamätaj si tieto kľúčové rady: Vždy si poriadne prečítaj úlohu (aj viackrát!), jasne si definuj neznámu a zapíš si, čo predstavuje.
Rozpoznávaj signálne slovíčka - "o viac/menej" znamená sčítanie/odčítanie, "krát viac/menej" znamená násobenie/delenie. Skúška správnosti nie je len formalita - je to tvoja poistka proti chybám!
Hlavné kroky si zopakuj: prečítať → zvoliť neznámu → vyjadriť údaje → zostaviť rovnicu → vyriešiť → skúška → slovná odpoveď. Drž sa tohto postupu a slovné úlohy už nebudú strašiak.
Keď toto zvládneš, matematika ti ukáže svoju skutočnú silu - pomôže ti riešiť reálne problémy zo života!
💡 Na záver: Cvič pravidelne a uvidíš, že preklad slov do rovníc bude čoraz jednoduchší!
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI Companion is a student-focused AI tool that offers more than just answers. Built on millions of Knowunity resources, it provides relevant information, personalised study plans, quizzes, and content directly in the chat, adapting to your individual learning journey.
Where can I download the Knowunity app?
You can download the app from Google Play Store and 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 Matematika
Most popular content
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
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
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
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
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 apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
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
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
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
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
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 apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
Riešenie Slovných Úloh Pomocou Lineárnych Rovníc
Slovné úlohy ťa strašia? Neboj sa! Vlastne sú to len príbehy z reálneho života, ktoré riešime pomocou matematiky. Keď sa naučíš prekladať slová do čísel a rovníc, zistíš, že nie sú také zlé.
Čo sú slovné úlohy a prečo sú dôležité
Predstav si, že matematika je ako prekladateľ - pomáha ti riešiť skutočné problémy zo života. Slovné úlohy sú presne takéto príbehy napísané slovami, ktoré musíš "preložiť" do matematického jazyka.
Väčšina týchto úloh ťa dovedie k lineárnej rovnici - to je rovnica, kde neznáma (zvyčajne x) nie je umocnená. Vyzerá napríklad takto: 2x + 5 = 11.
Kľúčové pojmy, ktoré musíš poznať: neznáma je to, čo hľadáš (označuje sa písmenom), riešenie rovnice je hodnota, ktorá rovnicu "vybalansuje", a skúška správnosti je overenie, či tvoj výsledok naozaj sedí.
💡 Tip: Na písomke určite budú, takže sa oplatí to pochopiť!
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Postup riešenia krok za krokom
Riešenie slovných úloh má jasné pravidlá. Keď ich budeš dodržiavať, nemôžeš sa pokaziť!
Najprv si úlohu poriadne prečítaj - aj dvakrát, ak treba. Zisti, čo už vieš (dané) a čo máš zistiť (hľadané). Potom si zvol neznámu - rozhodni, čo bude tvoje x a zapíš si to!
Ďalej vyjadri všetky údaje pomocou neznámej. Toto býva najťažší krok - musíš správne preložiť slová do matematiky. Napríklad "Janko má o 5 eur viac ako Marienka" znamená, že ak Marienka má x eur, Janko má x + 5 eur.
Nakonec zostav rovnicu - nájdi v úlohe nejakú rovnosť alebo vzťah. Ak "spolu majú 48 rokov", sčítaš ich veky a dáš to rovné 48.
💡 Pozor: "O 5 viac" = sčítanie, "trikrát viac" = násobenie!
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Dokončenie riešenia a skúška
Po zostavení rovnice ju vyrieš štandardnými postupmi - prenášaš členy cez rovnítko a dbáš na znamienka. Toto už zvládneš!
Skúška správnosti je kľúčová! Nedosadzuj len do rovnice, ale vráť sa k pôvodnej slovnej úlohe. Ak ti vyšlo, že syn má 12 rokov a otec 36, over si: je otec trikrát starší? (3 × 12 = 36 ✓) Majú spolu 48 rokov? (12 + 36 = 48 ✓)
Odpoveď musí byť slovná a musí odpovedať na otázku z úlohy. Nezabudni na jednotky! Nestačí napísať "x = 12", ale "Syn má 12 rokov a otec má 36 rokov."
Skontroluj si aj realitu výsledku - môže byť počet ľudí záporný? Určite nie! Ak ti vyjde niečo čudné, niekde je chyba.
💡 Dôležité: Vždy si zapíš, čo tvoje x predstavuje - bez toho sa ľahko stratíš!
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Riešený príklad: Súčet čísel po sebe
Skúsme si to na konkrétnom príklade! Úloha: Súčet troch po sebe idúcich prirodzených čísel je 63. Ktoré sú to čísla?
Môj postup: Prvé číslo označím ako x, druhé bude x + 1, tretie x + 2. Ich súčet je 63, takže: x + + = 63.
Riešenie rovnice: x + x + 1 + x + 2 = 63, čiže 3x + 3 = 63. Po úprave 3x = 60, takže x = 20. Hľadané čísla sú teda 20, 21, 22.
Skúška: 20 + 21 + 22 = 63 ✓ a sú to po sebe idúce čísla ✓. Odpoveď: Hľadané čísla sú 20, 21 a 22.
💡 Tip: Pri po sebe idúcich číslach si ušetríš prácu, keď prvé označíš ako x!
Sign up to see the contentIt's free!
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Improve your grades
Join milions of students
Ďalšie riešené príklady
Príklad s vekom: Otec je trikrát starší ako syn. Spolu majú 48 rokov. Koľko má kto rokov?
Syn má x rokov, otec má 3x rokov. Spolu: x + 3x = 48, čiže 4x = 48, takže x = 12. Odpoveď: Syn má 12 rokov, otec 36 rokov.
Príklad so žiakmi: V triede je 28 žiakov. Chlapcov je o 4 viac ako dievčat. Koľko je chlapcov a dievčat?
Dievčat je x, chlapcov x + 4. Spolu: x + = 28, čiže 2x + 4 = 28, takže 2x = 24 a x = 12. Odpoveď: 12 dievčat a 16 chlapcov.
Vidíš? Keď poznáš postup, lineárne rovnice z týchto úloh sa riešia úplne štandardne!
💡 Skúška vždy: 12 + 16 = 28 ✓, 16 - 12 = 4 ✓
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Dôležité tipy a záver
Pamätaj si tieto kľúčové rady: Vždy si poriadne prečítaj úlohu (aj viackrát!), jasne si definuj neznámu a zapíš si, čo predstavuje.
Rozpoznávaj signálne slovíčka - "o viac/menej" znamená sčítanie/odčítanie, "krát viac/menej" znamená násobenie/delenie. Skúška správnosti nie je len formalita - je to tvoja poistka proti chybám!
Hlavné kroky si zopakuj: prečítať → zvoliť neznámu → vyjadriť údaje → zostaviť rovnicu → vyriešiť → skúška → slovná odpoveď. Drž sa tohto postupu a slovné úlohy už nebudú strašiak.
Keď toto zvládneš, matematika ti ukáže svoju skutočnú silu - pomôže ti riešiť reálne problémy zo života!
💡 Na záver: Cvič pravidelne a uvidíš, že preklad slov do rovníc bude čoraz jednoduchší!
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI Companion is a student-focused AI tool that offers more than just answers. Built on millions of Knowunity resources, it provides relevant information, personalised study plans, quizzes, and content directly in the chat, adapting to your individual learning journey.
Where can I download the Knowunity app?
You can download the app from Google Play Store and 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 Matematika
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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
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
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
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
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 apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
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
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
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
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
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 apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user