Question

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

Answer 1

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