AMC 12 problem 1

Algebra Level 5

Define a function as, \(\displaystyle f\left( x,m \right) =\sum _{ n=1 }^{ m } \left| nx-1 \right| \).

Find the minimum value of \(f\left( x,119 \right)\).


This problem is rephrased from an AMC 12 test a few years back.
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