Question

已知有理数m,n,p,q在数轴上的位置如图1所示，且|m|=|n|. (1)|m+n|+|m+p|+|q-p|;

(2)|n-m|-3|m+p|-|-n-q|+|q-p|.

Answer 1

n>0,m<0,
|m|=|n|,-m=n,m+n=0;
n-m=2n>0

p>0,m<0,
|m|>|p|,-m>p,m+p<0,-(m+p)>0;

p>0,-p<0,
q<0,q-p<0,-(q-p)>0,

|m+n|+|m+p|+|q-p|
=0-(m+p)-(q-p)
=-m-p-q+p
=-m-q;【绝对值的和=-m-q>0】

n>0,m<0,|m|=|n|,-m=n,n-m=2n>0

p>0,m<0,
|m|>|p|,-m>p,m+p<0,-(m+p)>0;

n>0,q<0,|q|>|n|,
-q>n,
-n-q>n-n
-n-q>0;

p>0,-p<0,
q<0,q-p<0,-(q-p)>0,

|n-m|-3|m+p|-|-n-q|+|q-p|
=n-m-3*[-(m+p)]-(-n-q)+[-(q-p)]
=n-m+3m+3p+n+q-q+p
=2(m+n)+4p
=2*(0)+4p
=4p

追问

谢谢你！