Réponse :
Explications étape par étape
Bonjour
Résoudre les inéquations :
(-x + 1)(-x - 7) << 0
-x + 1 = 0 et -x - 7 = 0
x = 1 et x = -7
x............|-inf..........-7..........1...........+inf
-x + 1.....|........(+)..........(+)...o...(-)..........
-x - 7.....|........(+).....o...(-).........(-)..........
Ineq......|........(+).....o...(-)....o...(+)........
[tex]x \in [-7;1][/tex]
(3 - 2x)(1 - x) > 0
3 - 2x = 0 et 1 - x = 0
2x = 3 et x = 1
x = 3/2 et x = 1
x.............|-inf.........1........3/2.........+inf
3 - 2x.....|.......(+)........(+)..o....(-)...........
1 - x........|........(+)...o..(-)..........(-)..........
Ineq.......|........(+)...o..(-)...o....(+).........
[tex]x \in ]-\infty;1[ U ]3/2;+\infty[[/tex]
4x^2 - 9 << 0
(2x)^2 - 3^2 << 0
(2x - 3)(2x + 3) << 0
2x - 3 = 0 et 2x + 3 = 0
2x = 3 et 2x = -3
x = 3/2 et x = -3/2
x..............|-inf........(-3/2).........3/2,.........+inf
2x - 3.....|.......(-)................(-)....o......(+)........
2x + 3....|.......(-).......o.......(+)...........(+)........
Ineq.......|.......(+)......o........(-)....o.....(+)........
[tex]x \in [-3/2;3/2][/tex]
(x + 3)^2 - 4 >> 0
(x + 3)^2 - 2^2 >> 0
(x + 3 - 2)(x + 3 + 2) >> 0
(x + 1)(x + 5) >> 0
x + 1 = 0 et x + 5 = 0
x = -1 et x = -5
x..............|-inf...........(-5).........(-1)..........+inf
x + 1........|........(-).............(-).....o....(+).........
x + 5......|.........(-).......o....(+)..........(+)........
Ineq.......|.........(+)......o.....(-)....o....(+)........
[tex]x \in ]-\infty;-5] U [-1;+\infty[[/tex]
