Write the following inequalities in equivalent forms without the absolute values.
a1 is equivalent to b2:
a2 is equivalent to b5:
a3 is equivalent to b7:
a4 is equivalent to b10:
a5 is equivalent to b3:
a6 is equivalent to b8:
a7 is equivalent to b9:
a8 is equivalent to b4:
a9 is equivalent to b6:
a10 is equivalent to b1: and
. Thus, we must have
and
. The first of these inequalities requires
and
to both be positive or both be negative. Thus,
or
. The second requires
and
to have opposite signs. So,
. Combining these restrictions on
we have
(b1).
Commenting to point out a minor typo. For a5, the solution number is b3, not b5.
Thanks a lot for these solutions. They are a big help for me to go through this book.
Thanks! Fixed. No problem on making the solutions.