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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…..(+)……

(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….(+)………

(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….(+)……..