Sagot :
Réponse :
Explications étape par étape
Bonsoir
(3x-9)(-2x+1)>0
(3⋅x−9)⋅(−2⋅x+1)>0
3x-9 = 0 ou -2x+1=0
3x = +9 ou -2x = -1
X=9/3 = 3 ou x=-1/-2 = ½
x...........|-inf............1/2................3...........+inf
3x-9.....|.........(-)..............(-)..........o..(+)........
-2x+1....|.........(+).....o.....(-)...............(-).........
Ineq.....|..........(-)......o.....(+)........o...(-)........
S = ]1/2 ;3[
-2(7-x)(-3x-2) <=0
7 - x = 0 ou -3x - 2 = 0
7 = x ou 3x = -2
x = 7 ou x = -2/3
x...............|-inf..............(-2/3)..........7...........+inf
7 - x.........|.........(-)...................(-).....o....(+)..........
-3x-2.......|.........(+)..........o......(-)............(-)..........
Ineq.........|........(-)...........o......(+).....o.....(-).........
S = ]− ∞;−2/3]∪[7;+∞[
(x+7)/(2x-3)<=0
X+7 = 0 et 2x-3 # 0
x= -7 Et 2x # 3
x = -7 et x # 3/2
x...........| -inf............(-7)............3/2..........+inf
x + 7.....|.........(-)........o......(+)...........(+).........
2x - 3...|.........(-).................(-).....o.....(+)........
Ineq.....|..........(+)......o.......(-).....||.......(+)........
x € [7 ; 3/2[
(-3)/(4-2x)>0
4-2x # 0
2x # 4
x # 4/2
x # 2
x............|-inf.............2............+inf
4 - 2x....|..........(-).....o....(+).........
Ineq......|.........(-).......||.....(+)........
x € ]2 ; + inf[