a, ( x-1).( x+5)> 0
⇔ \(\left[ \begin{array}{l}\left \{ {{x-1>0} \atop {x+5>0}} \right.\\\left \{ {{x-1<0} \atop {x+5<0}} \right.\end{array} \right.\)
⇔ \(\left[ \begin{array}{l}\left \{ {{x>1} \atop {x>-5}} \right.\\\left \{ {{x<1} \atop {x<-5}} \right.\end{array} \right.\)
⇔ \(\left[ \begin{array}{l}x>1\\x<-5\end{array} \right.\)
b, ( x-2).( x-3)< 0
Dễ thấy x-2> x-3 ∀x
⇒ $\left \{ {{x-2>0} \atop {x-3<0}} \right.$
⇔ $\left \{ {{x>2} \atop {x<3}} \right.$
⇒ 2< x< 3
c, ( 3-x).( x+7)< 0
⇔ \(\left[ \begin{array}{l}\left \{ {{3-x>0} \atop {x+7<0}} \right.\\\left \{ {{3-x<0} \atop {x+7>0}} \right.\end{array} \right.\)
⇔ \(\left[ \begin{array}{l}\left \{ {{x<3} \atop {x<-7}} \right.\\\left \{ {{x>3} \atop {x>-7}} \right.\end{array} \right.\)
⇒ \(\left[ \begin{array}{l}x<-7\\x>3\end{array} \right.\)
d, ( 1-x).( x-4)> 0
⇔ \(\left[ \begin{array}{l}\left \{ {{1-x>0} \atop {x-4>0}} \right.\\\left \{ {{1-x<0} \atop {x-4<0}} \right.\end{array} \right.\)
⇔ \(\left[ \begin{array}{l}\left \{ {{x<1} \atop {x>4}(Vô lí)} \right.\\\left \{ {{x>1} \atop {x<4}} \right.\end{array} \right.\)
⇔ 1<x <4
