Assuming a and b are positive numbers, then
for the first inequality:
Both sides times , gives the first inequality.
for the second inequality:
Both sides divided by gives the second inequality.
We know from the right inequality that
We are now asking if
We can say...
by 2 times the amount that
We can examine the case for
the ratio is
The ratio is ,
therefore by a margin not greater than
the difference between and