Réponse :
Explications étape par étape
Bonjour
Résolvez les équations et inéquations suivantes :
1. 2x-1/5x+2= 0
(2x - 1)/(5x + 2) = 0
5x + 2 # 0
5x # -2
x # -2/5
2x - 1 = 0
2x = 1
x = 1/2
2. (2x-3)(x + 1) = (3-x)(x+ 1).
(2x - 3)(x + 1) - (3 - x)(x + 1) = 0
(x + 1)(2x - 3 - 3 + x) = 0
(x + 1)(3x - 6) = 0
(x + 1) * 3(x - 2) = 0
3(x + 1)(x - 2) = 0
x + 1 = 0 ou x - 2 = 0
x = -1 ou x = 2
3.(-x+5)*(3x+9)/7x+14 >=0
7x + 14 # 0
7x # -14
x # -14/7
x # -2
-x + 5 = 0 et 3x + 9 = 0
x = 5 et x = -3
x........|-inf......-3.........-2.........5.........+inf
-x+5..|.....(-).........(-).........(-)....o....(+).......
3x+9.|.....(-)....o...(+)........(+)..........(+)......
7x+14|.....(-)..........(-)....o..(+)..........(+).....
Ineq..|.....(-).....o...(+)...||...(-)....o.....(+).....
[tex]x \in [-3;-2[ U [5;+\infty[[/tex]
4. 1/x<3/2x+1
x # 0 et 2x + 1 # 0
x # 0 et x # -1/2
2x + 1 = 3x
1 = 3x - 2x
x = 1
5. (x/2+1) ^2= 121
(x/2 + 1)^2 - 121 = 0
(x/2 + 1)^2 - 11^2 = 0
(x/2 + 1 - 11)(x/2 + 1 + 11) = 0
(x/2 - 10)(x/2 + 12) = 0
x/2 - 10 = 0 ou x/2 + 12 = 0
x/2 = 10 ou x/2 = -12
x = 20 ou x = -24