已知-3<m<2.化简|m-2|+|m+3|-|3m+9|-|2m-4|

问题描述:

已知-3<m<2.化简|m-2|+|m+3|-|3m+9|-|2m-4|

原式=2-m+m+3-3m-9-4+2m=-8+2m

|m-2|+|m+3|-|3m+9|-|2m-4|
=2-m+m+3-3m-9-4+2m
=-m-8

|m-2|+|m+3|-|3m+9|-|2m-4|
=(2-m)+(m+3)-(3m+9)-(4-2m)
=2-m+m+3-3m-9-4+2m
=-m-8

-3<m<2
|m-2|+|m+3|-|3m+9|-|2m-4|
=|m-2|+|m+3|-3|m+3|-2|m-2|
=2-m+m+3-3(m+3)-2(2-m)
=5-3m-9-4+2m
=-8-m