How do solve #1/(x+2)>=1/3# algebraically?

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Answer 1 · 2016-09-12T07:26:49

#x in (-2, 1].#.

If #x>-2, x+2 is positive, Cross multiplication would not change the

in-between inequality sign. So,

#x+2<=3 to x <=1#.

And so, #x in (-2, 1].

When #x<-2, x+2<0#. Now, cross multiplication reverses the

inequality sign. So,

#x+2>=3 to x>=1#. As #x<-2#, this is an extraneous solution..

It follows that the answer is , #x in(-2, 1]#.