Question

If x>0, y>0, a x b, d y c, prove that: (a-d) |x| + |y| (b-c)

Answer 1

\[a\leq x \leq b\]
\[d \leq y \leq c\]
\[x>0,y>0\] and you want
\[a-d<|x| + |y| \leq b-c\] is that he problem?

Answer 2

i'm sorry it's y < 0

Answer 3

so maybe it would help if you wrote
\[a-d<x-y<b-c\]? not sure but it could

Answer 4

oh yes, you get it right away.

Answer 5

just subtract. you have
\[a<x<b\]
\[d<y<c\] subtract gives
\[a-d<x-y<b-c\] in one step.

Answer 6

okay. and then?