\marginnote misalignment in \begin{split}

Question

When I use \marginnote in \begin{equation}\end{equation}, it seems to work fine, but if I try to place a margin note inside a multiline equation (at least when I use \begin{split}\end{split}), there is a weird extra space between the first two lines of the margin note. I've attached a MWE so you can see what I mean. (I made the font smaller with \footnotesize so it is easier to see (and also because in practice I would like the font to be the size of footnotes anyways).)

\documentclass{article}

\usepackage{amsmath}
\usepackage{marginnote}

\begin{document}

\begin{equation}
\begin{split}
3x+2 & =\marginnote{\footnotesize{The solution is $x=1$.  Blah.  Blah.  Blah.  Blah.  Blah.  Blah.}}5 \\
4y-3 & =7.
\end{split}
\end{equation}

\end{document}

Answer 1

Put the marginnote before split (not inside). Further, as Gonzalo notes, changes to the font of marginnotes with the marginnote package are to be done using \marginfont. Also note that \footnotesize is a switch and it doesn't take any arguments.

 \documentclass{article}

\usepackage{amsmath}
\usepackage[fulladjust]{marginnote}
\renewcommand*{\marginfont}{\footnotesize}

\begin{document}

\begin{equation}
\marginnote{The solution is $x=1$.  Blah.  Blah.  Blah.  Blah.  Blah.  Blah.}
\begin{split}
3x+2 & =5 \\
4y-3 & =7.
\end{split}
\end{equation}

\end{document}