Bonjour
1. (5x - 3)(2x + 1)> (2x + 1) (x-4 )
(5x - 3)(2x + 1) - (2x + 1)(x - 4) > 0
(2x + 1)(5x - 3 - x + 4) > 0
(2x + 1)(4x + 1) > 0
2x + 1 = 0 ou 4x + 1 = 0
2x = -1 ou 4x = -1
x = -1/2 ou x = -1/4
x..............|-inf........-1/2........-1/4........+inf
2x + 1......|......(-)......o...(+)..........(+).........
4x + 1.....|.......(-)............(-).....o.....(+)........
Ineq.......|.......(+).....o....(-).....o.....(+).......
[tex]x \in ]-\infty ; -1/2[ U ]-1/4 ; +\infty[[/tex]
2. (3x + 2)(-6x – 1)> (3x + 2)2
(3x + 2)(-6x - 1) - (3x + 2)^2 > 0
(3x + 2)(-6x - 1 - 3x - 2) > 0
(3x + 2)(-9x - 3) > 0
(3x + 2) * 3(-3x - 1) > 0
3(3x + 2)(-3x - 1) > 0
3x + 2 = 0 ou -3x - 1 > 0
3x = -2 ou 3x = -1
x = -2/3 ou x = -1/3
x..............|-inf........-2/3........-1/3.........+inf
3x + 2.....|.......(-).....o....(+)..........(+)...........
-3x - 1.....|.......(+)...........(+).....o....(-)..........
Ineq.......|........(-).....o.....(+)....o.....(-)........
[tex]x \in ]-2/3 ; -1/3[[/tex]
3. (2x - 1)(-5x + 7) < 4x2 - 4x +1
(2x - 1)(-5x + 7) < (2x)^2 - 2 * 2x * 1 + 1^2
(2x - 1)(-5x + 7) < (2x - 1)^2
(2x - 1)(-5x + 7) - (2x - 1)^2 < 0
(2x - 1)(-5x + 7 - 2x + 1) < 0
(2x - 1)(-7x + 8) < 0
2x - 1 = 0 ou -7x + 8 = 0
2x = 1 ou 7x = 8
x = 1/2 ou x = 8/7
x.............|-inf..........1/2........8/7...........+inf
2x - 1.....|.......(-)......o....(+)..........(+)............
-7x + 8..|.......(+)............(+)....o.....(-)..........
Ineq......|........(-).....o.....(+)....o.....(-)..........
[tex]x \in ]-\infty ; 1/2[ U ]8/7 ; +\infty[[/tex]
