4
{x²+x-6)≥0⇒(x+3)(x-2)≥0⇒x≤-3 U x≥2
{x²-x-6≤0⇒(x-3)(x+2)≤0⇒-2≤x≤3
x∈[2;3]
5
[x²-x≤0⇒x(x-1)≤0⇒0≤x≤1
[x²-1>0⇒(x-1)(x+1)>0⇒x<-1 U x>1
x∈(-∞;-1) U [0;∞)
6
(x²+5x+18)/(x-4)+2>0
(x²+5x+18+2x-8)/(x-4)>0
(x²+7x+10)/(x-4)>0
(x+2)(x+5)/(x-4)>0
x=-2 x=-5 x=4
_ + _ +
---------------(-5)--------------(-2)----------------(4)---------------
x∈(-5;-2) U (4;∞)