equation, equation number and itemize bullet all on the same line

equation, equation number and itemize bullet all on the same line

I think the following sample says it all. I need to get the item bullet in
the right place on the same line as the equation, and have this followed
by an normal equation number. Someone asked the same question but the
answers all give one of the undesired results exhibited below. This
problem crops up a lot if you are writing lists of conditions and some
need a text Preamble while some are just equations. Thanks for any help
anyone can offer.
\documentclass{article}
\begin{document}
\begin{itemize}
\item This item looks fine in terms of both number and bullet because the
bullet sensibly appears on a line with some text on it, preceeding an
equation like
\begin{equation}
2+2=4,
\end{equation}
but if there is no text in the item there is no way to get it right, for
example
\item
\begin{equation}
2+2=4;
\end{equation}
The bullet is on the wrong line.
\item $\displaystyle 2+2=4;$ \\
No equation number.
\begin{equation}
\bullet \quad 2+2=4.
\end{equation}
Bullet in wrong position.
\end{itemize}
\end{document}