Question

решите неравенство 0,5<2^1-x<32

Answer 1

$0,5\ \textless \ 2^{1-x}\ \textless \ 32\\\\ \frac{1}{2}\ \textless \ 2^{1-x}\ \textless \ 2^5\\\\2^{-1}\ \textless \ 2^{1-x}\ \textless \ 2^5\; \; \Rightarrow \; \; \; -1\ \textless \ 1-x\ \textless \ 5\\\\-2\ \textless \ -x\ \textless \ 4\; |\cdot (-1)\\\\-4\ \textless \ x\ \textless \ 2\\\\x\in (-4,2)$

Answer 2

0,5<2^(1-х)<32
2(-1)<2^(1-х)<2^5
-1<(1-х)<5
-1<-(х-1)<5
-5<х-1<1
-4<х<2