Question 1009728: 1/x+3 + 1/x >_ 0
PLEASE HELP
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! Two critical points are -3 and 0.
Set 1/(x+3)>=(-1/x)
x>=-x-3
2x>=-3
x>=-3/2. that is another key point.
x<-3, pick -4
(-1)+(-1/4) not >=0, so not in interval
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pick -2
1-1/2 is >=0
-3/2 works (2/3)-(2/3)=0
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between -3/2 and 0, however, it does not work.
x=-1
1/2-(1)=-1/2.
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When x >=0, then it works, since both are positive,
(-oo,-3) does not work
(-3,-1.5} works
[0,oo) works
(-3,-1.5] U [0,oo)
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