I believe this comes from a textbook. Usually there are more than one solution for this type of question.

a) Rearrange,
(2-a)x<3-b and (5-c)x<3
To ensure x<-2, let a=1, b=5,c must be less than 5 so choose 4, you get
x<-2 and x<3 which gives x<-2

b) Same technique, rearrange.
(2-a)x<3-b and (5-c)x<3
Notice that if you make c=6, you get -x<3 which then produces x>-3
Now, when you make b=-1 and a=1, the left inequality simplifies into x<4.
Combine both, you get -3<4

c) This is easier than previous parts.
let c=6, you get x>-3
Let a=1, b=6, you get x<-3
This would not produce any solution as there isnt a number that would satisfy both inequalities at the same time.