My question is to find the minimum value of $$|x-1|+|3x-1|+|5x-1|+|7x-1|+|9x-1|+|11x-1|$$ One way is to find the minimum value using graph by which I got the answer $X=\frac{1}{9}$
But I want to know a simpler way to do it and for it I tried solving it using traingle inequality but wasn't getting the right answer so can anyone provide any simpler method or provide explanation how to solve using traingle inequality