Question

How do you solve `6/x+2>=0`?

Answer 1

`x>0` and `x leq -3`

Explanation:

Notice that this inequality is defined for `xne 0`.

By simple calculation we reduce to the form we need to study:

`1/xgeq -1/3`

so if `x>0` it is always true.

Let `x<0`, so multiplying by `x` affects the sign:

`1/xgeq -1/3 Leftrightarrow 1leq-1/3x Leftrightarrow -3 geq x`