Question

Решите неравенство: |1-2х|<5

Answer 1

$|T|\ \textless \ U\ \ \ \ \textless \ -\ \textgreater \ \ \ \ -U\ \textless \ T\ \textless \ U\\\\ |-T|=|T|$

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$|1-2x|\ \textless \ 5\\\\ |-(2x-1)|\ \textless \ 5\\\\ |2x-1|\ \textless \ 5\\\\ -5\ \textless \ 2x-1\ \textless \ 5\\\\ -5+1\ \textless \ 2x-1+1\ \textless \ 5+1\\\\ -4\ \textless \ 2x\ \textless \ 6\\\\ -2\ \textless \ x\ \textless \ 6\\\\ x\in(-2;\ 6)$