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# Translate inequalities involving absolute values to inequalities without absolute values

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).

### 2 comments

1. Jacare says:

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.

• RoRi says:

Thanks! Fixed. No problem on making the solutions.