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

Apr 20, 2017

$x > 0$ and $x \le q - 3$

#### Explanation:

Notice that this inequality is defined for $x \ne 0$.

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

$\frac{1}{x} \ge q - \frac{1}{3}$

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

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

$\frac{1}{x} \ge q - \frac{1}{3} \Leftrightarrow 1 \le q - \frac{1}{3} x \Leftrightarrow - 3 \ge q x$