Expert: Ahmed Salami - 7/23/2009

Question
I got this information from an A level book.
It says that " we can square both sides for |2x-3|<x+1 ; but not for the case |2x-3|>x+1. "
Can i know why is that so?
Thank you very much

Answer
Hi Kok,
First, you have to remember that |2x-3| is a positive quantity. In the first case it is less than x+1 which means that x+1 is also positive. So you can go on with the squaring to remove the absolute value sign and then go on to complete the solution.
But in the second case |2x-3| is greater than x+1, which means that we cant tell if x+1 is also positive or negative. Going on to square both sides is mathematically deficient.
Consider the statements;
|4| > -9    (which is true)
but is (|4|)^2 > (-9)^2 ?
Absolutely not, so i think you have your answer there.

Regards.