The set of real values of x for which log _0.2 (x+2)/x ≤ 1 is:

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