Question 97110

x^2 -5x -6 <=0

factorising the left hand side of the expression 

(x-6)(x+1) <=0

the product of 2 numbers will be <=0 when one is >=0 and the other <=0

case 1
 x-6 <=0     and x+1 >=0

gives x<=6 and x>= -1

Solution set is [-1,6]
ie -1<=x<=6

case 2 
 x-6 >=0 and x+1 <=0
gives 
 x>=6 and x<= -1 
which does not hold true for any x 

hence the only solution is [-1,6]
ie -1<=x<=6