y=|1-x|+|2-3x|+|3-4x|+|4-5x|+|5-6x|+|6-7x|
分段讨论：
1、当x≥1时
y=x-1+3x-2+4x-3+5x-4+6x-5+7x-6=26x-21
y≥5
2、当6/7≤x≤1时
y=-(x-1)+3x-2+4x-3+5x-4+6x-5+7x-6=24x-19
y≥11/7
3、当5/6≤x≤6/7时
y=-(x-1)+3x-2+4x-3+5x-4+6x-5-(7x-6)=10x-7
y≥4/3
4、当4/5≤x≤5/6时
y=-(x-1)+3x-2+4x-3+5x-4-(6x-5)-(7x-6)=-2x+3
y≥4/3
5、当3/4≤x≤4/5时
y=-(x-1)+3x-2+4x-3-(5x-4)-(6x-5)-(7x-6)=-12x+11
y≥7/5
6、当2/3≤x≤3/4时
y=-(x-1)+3x-2-(4x-3)-(5x-4)-(6x-5)-(7x-6)=-20x+17
y≥2
7、当x≤2/3时
y=-(x-1)-(3x-2)-(4x-3)-(5x-4)-(6x-5)-(7x-6)=-26x+21
y≥11/3
因此,当3/4≤x≤6/7时,y取得最小值
x=5/6,y=4/3