(3-|x|)/(|x|+2|)>=1/2
(3-|x|)/(|x|+2|)-1/2>=0
(4-3|x|)/(2|x|+4)>=0
所以(4-3|x|)(2|x|+4)>=0
(3|x|-4)(2|x|+4)<=0
所以-2<=|x|<=4/3
|x|>=0
0<=|x|<=4/3
所以-4/3<=x<=4/3