Answer
The solution is $x=\dfrac{6}{5}$.
Work Step by Step
Use the property $a^m = a^n \longrightarrow m=n$ to obtain:
$\begin{array}{ccc}
&1-2x&=&3x-5
\\&1-2x+2x&=&3x-5+2x
\\&1&=&5x-5
\\&1+5&=&5x-5+5
\\&6&=&5x
\\&\dfrac{6}{5} &= &\dfrac{5x}{5}
\\&\dfrac{6}{5}&=&x
\end{array}$
Thus, the solution is $x=\dfrac{6}{5}$.