Download - Inecuatii de Gradul I_2
![Page 1: Inecuatii de Gradul I_2](https://reader035.vdocumente.com/reader035/viewer/2022081719/55721089497959fc0b8d5305/html5/thumbnails/1.jpg)
Functia de gradul IFunctia de gradul IFunctia de gradul IFunctia de gradul I
Inecuatii de gradul IInecuatii de gradul I
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Definitie
• Prin inecuatie de gradul I intelegem o expresie de forma:
0a ,, unde ,0
sau 0
sau 0
sau 0
babxa
bxa
bxa
bxa
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Metode de rezolvare
• Metoda 1. Transformari echivalente
• Metoda 2. Semnul functie de gradul I
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Metoda 1. Transformari echivalente
• Pas 1. Efectuarea calculelor in fiecare membru, daca este cazul;
• Pas 2. Separarea termenilor;• Pas 3. Determinarea multimii
solutiilor:•Cazul I. => multimea solutiilor•Cazul II. => se inmulteste ecuatia
cu “-1” si se determina multimea solutiilor
Metode
0a0a
Exemplu
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Metoda 2. Semnul functie de gradul I
• Pas 1. Efectuarea calculelor in fiecare membru, daca este cazul.
• Pasul 2. Se trec toti termenii intr-un singur membru si se efectueaza calculele.
• Pasul 3. Se asociaza functia de gradul I.• Pasul 4. Se determina semnul functiei.• Pasul 5. Se determina multimea solutiilor.
MetodeExemplu
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AplicatieRezolvati inecuatia de mai jos (folosind cele 2 metode de rezolvare):
2523534 xx
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Rezolvare – Pasul 1Inecuatia:
2523534 xx
se rezolva si se ajunge la:Alegeti intre:
17674 xx
13674 xx
Nicio varianta de mai sus nu este corecta.
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Metoda 1 – Pasul 2Alegerea facuta este:
Dupa separarea termenilor.Alegeti intre:
17674
21565124 2523534
xx
xxxx
102 x
102 x
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Metoda 1 – Pasul 3Alegerea facuta este:
Deci pentru inecuatia multimea de solutii este:
Alegeti intre:
102
7176417674
x
xxxx
2523534 xx
]5,(x
),5[ x
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Metoda 1 – Raspuns
Alegerea facuta este:
]5,(
5 2
10 102 1- 102
x
xxxx
Felicitari, ati ales raspunsul corect!
![Page 11: Inecuatii de Gradul I_2](https://reader035.vdocumente.com/reader035/viewer/2022081719/55721089497959fc0b8d5305/html5/thumbnails/11.jpg)
AplicatieRezolvati inecuatia de mai jos (folosind cele 2 metode de rezolvare):
2523534 xx
![Page 12: Inecuatii de Gradul I_2](https://reader035.vdocumente.com/reader035/viewer/2022081719/55721089497959fc0b8d5305/html5/thumbnails/12.jpg)
Rezolvare – Pasul 1Inecuatia:
2523534 xx
se rezolva si se ajunge la:Alegeti intre:
17674 xx
13674 xx
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Metoda 2 – Pasul 2
Dupa efectuarea calculelor si trecerea termenilor intr-un singur membru obtinem:
Alegeti intre:
0102 x
0102 x
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Metoda 2 – Pasul 3
Asociem functia de gradul I:
102)( ,: xxff
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Dupa rezolvarea ecuatiei obtinem:
Alegeti intre:
0)( xf
Metoda 2 – Pasul 4.1
5x
5x
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Metoda 2 – Pasul 4.2Alegerea facuta este:
Iar tabelul de semn:
Alegeti intre:
5x
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Metoda 2 – Pasul 5
Pentru inecuatia multimea de solutii este:
Alegeti intre:
2523534 xx
]5,(x
),5[ x
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Metoda 2 - Raspuns
Felicitari, ati ales raspunsul corect!