Question

Ajuuuuuuuuuuutoooooooooooor........................!

Answer 1

a) (9x+3)(x-4)>9x²+x+5
⇒9x²-36x+3x-12>9x²+x+5
9x²-9x²-33x-x>5+12
-34x>17      ·-1
x<17/34
x<1/2
x∈(-α,1/2)

2x-3-(x-3)≤5
2x-3-x+3≤5
x≤5
x∈[5,+α)
deci x∈(-α,1/2)U[5,+α)

b) 12x²-(2x-3)(6x+1)>x
12x²-(12x²+2x-18x-3)>x
12x²-12x²+16x+3>x
16x-x>-3
15x>-3
x>-3/15
x>-1/5
x∈(-1/5,+α)

(5x-1)(5x+1)-25x²>x-6
25x²-1-25x²>x-6
-x>-6+1
-x>-5     ·-1
x<5
x∈(-α,5)
deci x∈(-1/5,5)