Question

Объясните, как найти множество решений неравенства:
log0.2((2x - 10)/(x + 11)) >= 0

Answer 1

$log_{0,2}\frac{2x-10}{x+11} \geq 0 \\ \\ 0\ \textless \ \frac{2x-10}{x+11} \leq 1\\ \\ \begin{cases} \frac{2x-10}{x+11}\ \textgreater \ 0 \\ \frac{2x-10}{x+11} \leq 1 \end{cases} \ \textless \ =\ \textgreater \ \begin{cases} \frac{x-5}{x+11}\ \textgreater \ 0 \\ \frac{2x-10-x-11}{x+11} \leq 0 \end{cases} \ \textless \ =\ \textgreater \ \begin{cases} \frac{x-5}{x+11}\ \textgreater \ 0 \\ \frac{x-21}{x+11} \leq 0 \end{cases} =\ \textgreater \ \\ \begin{cases}x \in (-\infty; -11) \cup (5;+\infty) \\ x \in (-11;21] \end{cases} =\ \textgreater \ \boxed {x \in (5;21].}$