Question

Подскажите, пожалуйста, каким образом решается данное неравенство?

Answer 1

$5000^{1-x}\ \textgreater \ 5001^{1-x} \\ \\ \frac{5000}{5000^\textup{x}} \ \textgreater \ \frac{5001}{5001^\textup{x}} \\ \\ 5000\cdot5001^x\ \textgreater \ 5001\cdot5000^x~~~|:5000 \\ \\ 5001^x\ \textgreater \ \frac{5001\cdot5000^x}{5000} ~~~|:5001\\ \\ \frac{5001^x}{5001} \ \textgreater \ \frac{5000^x}{5000} \\ \\ 5001^{x-1}\ \textgreater \ 5000^{x-1}~~~|:5000^{x-1} \\ \frac{5001^{x-1}}{5000^{x-1}} \ \textgreater \ 1 \\ \\ ( \frac{5001}{5000} )^{x-1}\ \textgreater \ ( \frac{5001}{5000} )^0$

$x-1\ \textgreater \ 0 \\ x\ \textgreater \ 1$

Ответ: $x\in(1;+\infty)$