则｜x-1｜+｜x-3｜
=｜1-1｜+｜1-3｜
= 0+2
= 2
若x=3,
则｜x-1｜+｜x-3｜
=｜3-1｜+｜3-3｜
= 2+0
= 2
若x=2
则｜x-1｜+｜x-3｜
=｜2-1｜+｜2-3｜
= 1+1
=2
但 若x＜1或x＞3
如x=0,
则｜x-1｜+｜x-3｜
=｜0-1｜+｜0-3｜
= 1+3
= 4
如x=-1,
则｜x-1｜+｜x-3｜
=｜-1-1｜+|-1-3｜
= 2+4
=6
如x=4,
则｜x-1｜+｜x-3｜
=｜4-1｜+｜4-3｜
=3+1
=4
∴x只能是不小于1且不大于3的有理数
∴｜x-1｜+｜x-3｜的最小值是2.