I had the following task at one of the math exams. It went something like this. Real number x is closer to 'a' than it is to 'b'. Write that in terms of... Soo I wrote |x-a| < |x-b| the task continued Specify the interval for which all values of x are closer to 4 than are to -1. Soo one way would be to put a = 4 and b = -1 in the equation to get |x-4| < |x+1| but I am not very fond on solving this equation if I can make a more easy equation to do the trick. Since geometrically all what I have to do is find the the point that is equidistand from a and b. That is x = (a+b)/2 and then it simply a matter of going left or right on the number axis. I just wrote the solution to be x in interval (a+b)/2, inf -> (4-1)/2 , inf -> x in interval of (3/2, inf] is closer to 4 than to -1. That is the correct answer, all values of x that are greater than x =3/2 lie closer to 4 than to -1. Now I guess for mathematitian this is more of a guessing than a formal solution of a problem. Soo should I be required to prove what I just did or is it acceptable?