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