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

How do solve 1/(x+2)>=1/31/(x+2)>=1/3 algebraically?