Réponse :
Bonjour
Explications étape par étape
2 - 3x = 0
3x = 2
x = 2/3
2x^2 + 3 toujours positif quelque soit x
x..............|-inf..................2/3...............+inf
2-3x.......|...........(+)...........o.......(-).............
2x^2+3..|...........(+).....................(+)...........
Ineq.......|............(+)...........o.......(-)..............
S = [2/3 ; +inf [
x^2 < 4
x^2 - 4 < 0
(x - 2)(x + 2) < 0
x - 2 = 0 => x = 2
x + 2 = 0 => x = -2
x.............| -inf.............(-2).............(2)........+inf
x - 2.......|...........(-)................(-).......o....(+).......
x + 2......|...........(-).......o.......(+)............(+).......
Ineq......|............(+)......||........(-)......||......(+)......
S = ] -2 ; 2 [
(4x - 3)^2 << 0
Pas de solution car un carré est toujours positif
-2(x + 5)(2x - 7) < 0
x + 5 = 0 => x = -5
2x - 7 = 0 => 2x = 7 => x = 7/2
x...........| -inf..........(-5)..........(7/2)........+inf
x + 5....|.........(-)......o.....(+)............(+).........
2x - 7..|.........(-)..............(-)......o.....(+).........
Ineq....|.........(+)......||.....(-)......||......(+).........
S = ] -5 ; 7/2 [
