|x-a|+|x-b| represents the sum of distances from x to points a and b. Minimum value = |a-b| (the distance between the two points), achieved when x is between a and b (i.e., a<=x<=b or b<=x<=a). For |x-a|+|x-b|+|x-c| (a<b<c): minimum at x=b (the median), value = |a-b|+|c-b| = c-a. General rule: for n terms |x-a1|+...+|x-an|, the minimum occurs at the median of {a1,...,an}. For even n, any x between the two middle values achieves the minimum. This is a frequent JEE optimization trick.