$9.219 \frac{3^{2|x-1|}+3}{4}<3^{|x-1|}$

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$9.219 \frac{3^{2|x-1|}+3}{4}<3^{|x-1|}$
## Solution.

$3^{2|x-1|}-4 \cdot 3^{|x-1|}+3<0 \Leftrightarrow\left(3^{|x-1|}-1\right)\left(3^{|x-1|}-3\right)<0 \Leftrightarrow$
$\Leftrightarrow 3^{0}<3^{|x-1|}<3^{1} \Leftrightarrow 0<|x-1|<1 \Leftrightarrow\left\{\begin{array}{l}-1<x-1<1, \\ x \neq 1 .\end{array}\right.$

Answer: $x \in(0 ; 1) \cup(1 ; 2)$.