Answer:
-1, -2, -3, etc (all negative numbers).
Explanation:
We will put numbers in for n, begin with 0. 6[2(0)+3]<3-[4(0)-3], 6(0+3)<3-(0-3), 6(3)<3-(-3), two negative make a positive, so 3-(-3) will be 3(3), 18<9, 0 is not a solution. Let put 1 in this time, 6[2(1)+3]<3-[4(1)-3], 6(2+3)<3-(4-3), 6(5)<3-(1), 3-(1) is the same as 3(-1), 30<-3, 1 is not a solution. Since the numbers are going in different direction (18<9, 30<-3) one is going bigger in positive the other one had gone to negative, we can expect the positive will keep go bigger in positive while the negative will go bigger in negative. In this case we will do negative numbers instead of positive, begin with -1, 6[2(-1)+3]<3-[4(-1)-3], 6(-2+3)<3-(-4-3), 6(1)<3-(-7), like 3-(-3) two negative make a positive, so 3-(-7) will be 3(7), 6<21, -1 is a solution if -1 works the rest of the negative numbers will also. So the answer is all the negative numbers