Answer to Question #28760 in Integral Calculus for Ankit

Question

-1/modulusx-2 >_1

Answer 1

-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