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.