# Align long text under itself in enumerate list

Problem:

I have a long text that is split into two sentences in a enumerate list. I wish for the text to be vertically center aligned with the item.

Minimal Working Example (MWE):

\documentclass{article}
\usepackage{enumitem}
\usepackage{amsmath}

\begin{document}

\noindent
\begin{enumerate}[label=\textbf{\arabic*}), itemsep=3ex]
\item $\dfrac{3x + 1}{x - 1} \geq \dfrac{6x - 2}{x + 2} \Leftrightarrow \dfrac{3x + 1}{x - 1} - \dfrac{6x - 2}{x + 2} \geq 0 \Leftrightarrow (MGN = (x - 1)(x + 2))$
\item[] $\Leftrightarrow \dfrac{(3x + 1)(x + 2)}{(x - 1)(x + 2)}-\dfrac{(6x - 2)(x - 1)}{(x + 2)(x - 1)} \geq 0 \Leftrightarrow$ (This is a short sentence.)
\item[] $\Leftrightarrow \dfrac{(3x + 1)(x + 2) - (6x - 2)(x - 1)}{(x - 1)(x + 2)} \geq 0 \Leftrightarrow$ (This is a long sentence that needs be beneath itself.)
\item[] $\Leftrightarrow \dfrac{3x^{2} + 7x + 2 - \left(6x^{2} - 8x + 2\right)}{(x - 1)(x + 2)} \geq 0 \Leftrightarrow R(x) = \dfrac{-3x^{2} + 15x}{(x - 1)(x + 2)} \geq 0$
\end{enumerate}
\end{document}

Current output:

Desired output:

The text This is a long sentence that needs be beneath itself. should be under itself aligned vertically center to the right of the double arrow.

\documentclass{article}
\usepackage{enumitem}
\usepackage{amsmath}

\begin{document}

%? \noindent
\begin{enumerate}[label=\textbf{\arabic*}), itemsep=3ex]
\item $\dfrac{3x + 1}{x - 1} \geq \dfrac{6x - 2}{x + 2} \Leftrightarrow \dfrac{3x + 1}{x - 1} - \dfrac{6x - 2}{x + 2} \geq 0 \Leftrightarrow (MGN = (x - 1)(x + 2))$
\item[] $\Leftrightarrow \dfrac{(3x + 1)(x + 2)}{(x - 1)(x + 2)}-\dfrac{(6x - 2)(x - 1)}{(x + 2)(x - 1)} \geq 0 \Leftrightarrow$ (This is a short sentence.)
\item[] $\Leftrightarrow \dfrac{(3x + 1)(x + 2) - (6x - 2)(x - 1)}{(x - 1)(x + 2)} \geq 0 \Leftrightarrow$ \parbox{4cm}{\centering (This is a long sentence that needs be beneath itself.)}
\item[] $\Leftrightarrow \dfrac{3x^{2} + 7x + 2 - \left(6x^{2} - 8x + 2\right)}{(x - 1)(x + 2)} \geq 0 \Leftrightarrow R(x) = \dfrac{-3x^{2} + 15x}{(x - 1)(x + 2)} \geq 0$
\end{enumerate}
\end{document}