I know how to solve this task but I have certain things that I do not understand.
Because |x-3| occurs on the right side of this "if statement", it will be helpful to factor the left side to introduce a factor of |x-3|.
Using the triangle inequality:
By multiplying the statement above with |x-3| (which is positive) we got:
Now clearly and
By multiplying both inequalities (I am not sure if this step is valid, please confirm me) I got:
We can conclude that:
Now isn't ??
Why in my book they choose ?
And why they choose and with that restriction
Finally I don't understand why .
Could somebody possibly explain?
Thanks a lot.