This solution and process is WRONG! The solution to this is ALL REAL NUMBERS! At any step along the process, the abolute value will evaluate to a non-negative number (at least zero). You actually don't even need to work the problem. If you don't believe me, try a number OUTSIDE of the solution interval given-- like 10 for example. The inequality is true no matter what!! This is a special case.
I am a math professor with a MS in Mathematics.