n is an integer such that 6-3n>18 and (-5n)/(n^2-6)>1. Find all the possible values of n.

First we solve 6-3n>18. We do this by rearranging:Carry over the -3n term for 6>18+3n.Take away 18 from both sides for -12>3n.Divide both sides by 3 for -4>n.So we know that n<-4. Now we solve (-5n)/(n^2-6)>1. We do this by rearranging the equation into the form an^2+bn+c(<0):Multiply each side by (n^2-6) for -5n>n^2-6.Move the -5n term to the other side of the equation for n^2+5n-6<0.Factorise the quadratic for (n+6)(n-1)<0.We then look at the graph of the quadratic to solve the inequality for -6<n<1.So the possible values of n must satisfy the inequalities n<-4 and -6<n<1. Hence, we can conclude that -6<n<-4, so the only possible value of n is n=-5.