Question

If a < b and c > d, prove a - c > b - d

Answer 1

sorry, it should be prove a - c < b - d

Answer 2

a<b
d<c
a+d<b+d<b+c
a+d<b+c
a+(-c)+d<b+c+(-c)
a+(-c)+d<b
a+(-c)+d+(-d)<b+(-d)
a-c<b-d

Answer 3

hmmm looks okay

Answer 4

I think we need to know that a, b and c are each positive, otherwise things might go wrong.

How about a<b, so a-c<b-c<b-d, because c>d?