The set of real values of x for which $\log _{0.2} \frac{x+2}{x} \leq 1$ is:

$\left(-\infty, \frac{-5}{2}\right] \cup(0,+\infty)$

$\log _{0.2} \frac{x+2}{x} \leq 1⇒\frac{x+2}{x} \geq \frac{1}{5}$  as base =  0.2<1

so $ \frac{x+2}{x}-\frac{1}{5}≥0⇒\frac{5x+10-x}{5x}≥0$

$⇒\frac{4x+10}{5x}≥0⇒\left(-\infty, \frac{-5}{2}\right] \cup(0,\infty)$

by wave curve method