Question

|9-x|> 21 в виде двойного неравенства

Answer 1

$|T|\ \textgreater \ U\\\\ T\ \textgreater \ U\ \ \ or\ \ \ T\ \textless \ -U$
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также $|-A|=|A|$
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$|9-x|\ \textgreater \ 21\\\\ |-(x-9)|\ \textgreater \ 21\\\\ |x-9|\ \textgreater \ 21\\\\ x-9\ \textgreater \ 21\ \ \ or\ \ \ x-9\ \textless \ -21\\\\ x\ \textgreater \ 30\ \ \ or\ \ \ x\ \textless \ -12\\\\ x\in(30;\ +\infty)\ \ \ or\ \ \ x\in(-\infty;\ -12)\\\\ x\in(-\infty;\ -12)\cup(30;\ +\infty)$

ответ: $(-\infty;\ -12)\\\\ x\in(-\infty;\ -12)\cup(30;\ +\infty)$
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двойное неравенство возникает в случае:
$|T|\ \textless \ U\\\\ -U\ \textless \ T\ \textless \ U\\\\ --------------\\ |9-x|\ \textless \ 21\\ |x-9|\ \textless \ 21\\ -21\ \textless \ x-9\ \textless \ 21\\\\ -21+9\ \textless \ x\ \textless \ 21+9\\\\ -12\ \textless \ x\ \textless \ 30\\\\ x\in(-12;\ 30)$