Question

How to solve:|x-2| +|x-5|=3

Answer 1

Here's how I like to think about absolute value equations: The quantity inside the abs.val. bars can be positive or negative, so you have to consider both possibilities.

i.e. what if (x-2) and (x-5) are both positive, and what if (x-2) and (x-5) are both negative?

Answer 2

It's also possible that one of the quantities is negative and the other positive..

Answer 3

but we used to take only positive always