Find the minimum value of `|x|+|x+1/2|+|x-3|+|x-5/2|dot`

Answer

6

Explanation

`f(x)=|x|+|x+1/2|+x-3|+|x-5/2|`
`f(x)=-4x+5x," for "x le -1//2`
`=-2x+6," for "-1/2 le x le 0`
`=6" for "0 le x le 5/2`
`=2x+1," for "5/2 le x le 3`
`=4x-5" for "x ge 3`
From the graph, minimum value of the function is 6.