The minimum value of |x|+x+12+|x-3|+x-52 is

f(x)=|x|+x+12+|x-3|+x-52=-4x+5, for x≤-1/2=-2x+6, for -12≤x≤0=6, for 0≤x≤52=2x+1, for 52≤x≤3=4x-5, for x≥3 From the graph, minimum value of the function is 6 .