Posted by please help me out!! on Thursday, March 28, 2013 at 12:16pm.
As x ranges over all real values, what is the minimum value of f(x)=x−123+x−456+x−789?

ALGEBRA(Sum of Absolute Value Differences)  Steve, Thursday, March 28, 2013 at 1:30pm
Note that xa+xb is constant (ba) for a<=x<=b
So, since x123+x789 is constant for 123<=x<=789, the minimum occurs at x=456, and is 666.