|1-x|>=2x

if 2x>0 i.e x>0

The inquality can be simpfied to 1-x>=2x or 1-x<=-2x

1-x>=2x i.e x<=1/3
1-x<=-2x i.e x<=-1
so combine these two result,we can get:
x<=1/3

if 2x<=0 we can see the inquality is correct whatever x is.

so x<=0

we combine these two result,we get:
x<=1/3

若x>=1,1-x<=0,|1-x|=x-1
x-1>=2x
x<=-1
和x>=1矛盾，不成立

若x<1,1-x>0,|1-x|=1-x
1-x>=2x
3x<=1
x<=1/3
所以
x<=1/3

综上
x<=1/3

原不等式等价于1-x≥2x ①或1-x≤-2x ②
解①得x≤1/3
解②得X≤-1
原不等式的解集为{x|x≤1/3｝

绝对值不等式|f（x）|≥g（x）等价于f（x）≥g（x）或f（x）≤-g（x），利用这个可以解

=>1-x>=2x及x-1<=2x
=>3x<=1及x>=-1
=>x<=1/3及x>=-1

假设ㄧ1-xㄧ＜2x
两边平方,得:
(1-x)平方＜4x平方
化简得:
3x平方+2x-1＞0
根据△=b平方-4ac≥0,得
上式的△=4-12=-8＜0
上式无解,所以ㄧ1-xㄧ≥2x

2x<=1-x<=-2x;
-