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

Sep 12, 2016

$x \in \left(- 2 , 1\right] .$.

#### Explanation:

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

in-between inequality sign. So,

$x + 2 \le 3 \to x \le 1$.

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

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

inequality sign. So,

$x + 2 \ge 3 \to x \ge 1$. As $x < - 2$, this is an extraneous solution..

It follows that the answer is , $x \in \left(- 2 , 1\right]$.