Question

|a|-|a-b|+|c-b|+|a+c|怎么化简?

C=-2.5 B=-1.5 A=0.5

Answer 1

c<b<0 a>0
即a-b>0 c-b<0 a+c<0
则|a|-|a-b|+|c-b|+|a+c|=a-(a-b)-(c-b)-(a+c)=a-a+b-c+b-a-c=-a+2b-2c

下次麻烦先把数写出来 让我好判断

1.a>b>c>0
则a>0,a-b>0,c-b<0,a+c>0
|a|-|a-b|+|c-b|+|a+c|=a-(a-b)-(c-b)+a+c=a-a+b-c+b+a+c=a+2b
2.a>c>b>0与c>a>b>0情况一样
则a>0,a-b>0,c-b>0,a+c>0
|a|-|a-b|+|c-b|+|a+c|=a-(a-b)+(c-b)+a+c=a-a+b+c-b+a+c=a+2c
3.b>c>a>0与b>a>c>0情况一样
则a>0,a-b<0,c-b<0,a+c>0
|a|-|a-b|+|c-b|+|a+c|=a-[-(a-b)]-(c-b)+a+c=a+a-b-c+b+a+c=3a
4.c>b>a>0
则a>0,a-b<0,c-b>0,a+c>0
|a|-|a-b|+|c-b|+|a+c|=a-[-(a-b)]+(c-b)+a+c=a+a-b+c-b+a+c=3a-2b+2c
5.c>a>b>0
则a>0,a-b>0,c-b>0,a+c>0
|a|-|a-b|+|c-b|+|a+c|=a-(a-b)+(c-b)+a+c=a-a+b+c-b+a+c=a+2c
6.0>a>b>c
则a<0,a-b>0,c-b<0,a+c<0
|a|-|a-b|+|c-b|+|a+c|=-a-(a-b)-(c-b)-(a+c)=-a-a+b-c+b-a-c=-3a+2b-2c
7.0>a>c>b
则a<0,a-b>0,c-b>0,a+c<0
|a|-|a-b|+|c-b|+|a+c|=-a-(a-b)+(c-b)-(a+c)=-a-a+b+c-b-a-c=-3a
8.0>b>c>a
则a<0,a-b<0,c-b<0,a+c<0
|a|-|a-b|+|c-b|+|a+c|=-a-[-(a-b)]-(c-b)-(a+c)=-a+a-b-c+b-a-c=-a+2b-2c