In the first example, the textbook says we need the absolute value symbol because x might be negative
In the second example, the textbook doesn't include the absolute value symbol
What's the difference? When do we use absolute value and when not?
Yes, in order that exist (we are talking about real numbers here) x itself must non-negative so |x|= x.
For example, in the first problem, , if x= 3 or -3, we would have as well as . To cover both possibilities we must say .
But in the second problem, , if x= -3, that would be which is not a real number.