-1/|x|-2>=1 In interval notation we have the following: ________________0________________ So there are two intervals to be considered. Note that we exclude x=0 because we have x in the denominator, therefore it should be nonzero. 1)x<0 In this case we have -1/(-x)-2>=1 1/x-2>=1 1/x>=3 As x<0 this inequality has no solutions so we have empty set 2)x>0 we obtain -1/x-2>=1 -1/x>=3 1/x<=-3 1<=-3x x<=-1/3 Also we have x>0 so there's also empty set
Final answer is empty set.
Also we could do it another way. -1/|x|-2>=1 -1/|x|>=3 1/|x|<=-3 This is false because 1/|x|>0 for real x
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