# The Absolute's Minimum

Algebra Level 4

$\large |x - 1| + |2x-1| + |3x-1| + \cdots + |300x-1|$

If the minimum value of the expression above is $\dfrac AB$, and it occurs when $x = \dfrac CD$, where $(A, B)$ and $(C, D)$ are each coprime pairs of positive integers, find $A+B+C+D$.

×