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Nelly14
@Nelly14
May 2019
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Bonjour à tous , j'aimerais s'il vous plaît que vous m'aidiez à faire cette exercice. En utilisant un tableau de signes, résoudre les inéquations suivantes :
a) ( 3x + 3)(-5x+1) >0
b) (-7x+7)(x+2)<0
c) ( -2x+4)x <0
d) ( 3x+4) x au carré <0
Merci d'avance pour votre aide ♡
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no63
Salut
a) (3x+3)(-5x+1)>0
=> 3x+3>0 => 3x>-3 =>x>-1
=>-5x+1>0 => -5x>-1 => x<1/5
tableau
x -inf -1 1/5 +inf
3x+3 - 0 + +
-5x-1 + + 0 -
expr - 0 + 0 -
S= ] -1 ; 1/5 [
b) (-7x+7)(x+2)<0
=> -7x+7<0 => -7x<-7 => x>1
=> x+2<0 => x< -2
tableau
x -inf -2 1 +inf
x+2 - 0 + +
-7x+7 + + 0 -
expr - 0 + 0 -
S= ] -inf ; -2 [ U ] 1 ; +inf [
c) (-2x+4)x<0
=> -2x<-4 => x>2
tableau
x -inf 0 2 +inf
x - 0 + +
-2x+4 + + 0 -
expr - 0 + 0 -
S= ] -inf ; 0 [ U ] 2 ; +inf [
d) (3x+4)x²<0
=> 3x+4<0 => x< -4/3
tableau
x -inf -4/3 0 +inf
x² + + 0 +
3x+4 - 0 + +
expr - 0 + 0 +
S= ] -inf ; -4/3 [
0 votes
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Hey ! Et merci d'avance pour votre aide ^^
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a) (3x+3)(-5x+1)>0
=> 3x+3>0 => 3x>-3 =>x>-1
=>-5x+1>0 => -5x>-1 => x<1/5
tableau
x -inf -1 1/5 +inf
3x+3 - 0 + +
-5x-1 + + 0 -
expr - 0 + 0 -
S= ] -1 ; 1/5 [
b) (-7x+7)(x+2)<0
=> -7x+7<0 => -7x<-7 => x>1
=> x+2<0 => x< -2
tableau
x -inf -2 1 +inf
x+2 - 0 + +
-7x+7 + + 0 -
expr - 0 + 0 -
S= ] -inf ; -2 [ U ] 1 ; +inf [
c) (-2x+4)x<0
=> -2x<-4 => x>2
tableau
x -inf 0 2 +inf
x - 0 + +
-2x+4 + + 0 -
expr - 0 + 0 -
S= ] -inf ; 0 [ U ] 2 ; +inf [
d) (3x+4)x²<0
=> 3x+4<0 => x< -4/3
tableau
x -inf -4/3 0 +inf
x² + + 0 +
3x+4 - 0 + +
expr - 0 + 0 +
S= ] -inf ; -4/3 [