conform-algoritmului-propus,rezolva-exercitiile (in loc de N pui cifra 9 )
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Răspuns:
Exercitiul 3
l(x-9)/(x+9)l<3 x=/= -9
-3<(x-9)/(x+9)<3
Sistem
{-3<(x-9)/(x+9) => 0<(x-9)/(x+9)+3
Aduci la acelasi numitor
[(x-9)+3(x+9)]/(x+9).>0
(x-9+3x+27)/(x+9)>0
(4x+18)/(x+9)>0
4x+18=0 x= -18/4= -9/2
x l -∞...........-9..........-9/2...........0.............+∞
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4x+18 l- - - - - - - 0+ + + + +
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x+9 l- - - - 0+ + + + + +
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(4x+18)/(x+9)l + + l-- - - - - 0+ + +
Iei in considerare numai valorile pozitive
x∈(-∞, -9)U[-9/2, +∞) A
(x-9)/(x+9)<3
(x-9)/(x+9)-3<0
[(x-9)-3(x+9)]/(x+9)<0
(x-9-3x-27)/(x+9),<0
(-2x_36)/(x+9)<0 Impari inegalitatea prin -2 si schimbi semnul < in >
(x+18)/(x+9)>0
x+18=0 x= -18
tabelul de semne
x l-∞.............-18.............-9...........0.................+∞
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x+18 l- - - - - 0+ = + + + + +
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x+9 l- - - - -0 + + + + + + +
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(x+18)/(x+9)l + + 0- - - - l+ + + + + +
Iei in coonsiderare numai valorbile pozitive
x∈(-∞, -18]U(-9,+∞) (B
Intersectezi A cu B
x∈(-∞, -9)U[-9/2,+∞)∩(-∞ ,-18]U(-9 ,+∞)=(-∞,-18]U(-9/2,+∞)
Exercitiul 1
l3x-9l-l2x-1l>5
l3x-9l-l2x-1l-5>0
caz 1 3x-9>0 x.>1/3 2x-1>0 x>1/2
3x-9-2x+1-5>0
x-13>0 x>13
x∈(1/2,+∞)∩(1/3,∞)∩(13,∞)=(13,∞)
Caz 2
3x-9≥0 x>1/3 2x-1<0 x<1/2
3x-9+2x-1-5>0
5x>15
x>3
x∈[1/3,∞)∩(-∞,1/2)∩(3,∞)=Ф inecuatia nu are solutii
caz3
3x-9<0 x<1/3 2x-1≥0 x≥1/2 inecuatia devine
-3x+9-2x+1-5>0
-5x+5>0 x> -1
x∈(-∞,1/3)∩[1/2, +∞)∩(-1,∞)=(-1, 1/3)
Caz4
3x-1<0 x<1/3 2x-1<0 x<1/2 Inecuatia devine
-3x+1+2x-1-5>0
-x-5>0 -x>5 x< -5
x∈(-∞, 1/3)∩(-∞,1/2)∩(-∞, -5)=(-∞,-5)
Reunesti intervalele de la 1 , 2, 3, si 4 si obtii
x∈(-∞,-5)U(-1,1/3)U(13,∞)
Explicație pas cu pas: