Question

Prove
If x 13 years ago

Answer 1

well (x+y)/2 is the average of x and y, so if x<y it's bound to be larger than x and less than y
algebraically you can start with x<y
add x to both sides x+x < y+x
2x <y+x
then divide both sides by two x<(y+x)/2

Answer 2

you can do something very similar to show that (x+y)/2 <y

Answer 3

x<y
hence x/2<y/2
or x/2+x/2<y/2+x/2
or x<(x+y)/2

Answer 4

again
x<y hence x/2<y/2
x/2+y/2<y/2+y/2
or (x+y)/2 <y