Left align equation after intertext

Question

I wish to left align a part of my equation (the description of the variable used in the equation) after my intertext while keeping the main equation center aligned, as shown in Figure below...

Although I managed to do it using {equation} followed by {flalign*} this introduced 'linebreak' after the main equation which is centred (see 1st box).

I also tried using {flalign} with \noalign but this remove the equation numbering as well as producing a big gap between the equation (see 2nd box) and text which i wish to avoid...

Is there any ways to solve this issue?

My code is as follow:

\documentclass[a4paper,11pt,oneside]{memoir}    
\usepackage{mathtools}
\usepackage{lipsum}

\begin{document}
Case 1:\\
\lipsum[75]
\begin{equation}
x' = \overline{x} \pm u_{\overline{x}} \qquad(P\%)
\end{equation}
\begin{flalign*}
\shortintertext{where}
\qquad  \overline{x} &= \text{Most probable estimate of } x' \text{ based on the available data}    &\\
\qquad   \pm u_{\overline{x}} &= \text{Uncertainty interval in that estimate at some probability level, } P\%   &\\
\qquad  P &= \text{Probability level or confidence level} &
\end{flalign*}

Case 2:\\
\lipsum[66]
\begin{flalign}
\noalign{\centering $x' = \overline{x} \pm u_{\overline{x}} \qquad(P\%)$}
\shortintertext{where}
\qquad  \nonumber \overline{x} &= \text{Most probable estimate of } x' \text{ based on the available data}  &\\
\qquad  \nonumber \pm u_{\overline{x}} &= \text{Uncertainty interval at some probability level, } P\%   &\\
\qquad   P &= \text{Probability level or confidence level} &    
\end{flalign}


\end{document}

Answer 1

I suggest to define a subsidiary environment to gather:

\documentclass[a4paper,11pt,oneside]{memoir}
\usepackage{amsmath,array,tabularx}
\usepackage{lipsum}

\newlength{\wherewd}
\newenvironment{where}
 {%
  \minipage{\displaywidth}
  \settowidth\wherewd{where }
  where
  \tabularx{\dimexpr\textwidth-\wherewd}[t]{
    @{}
    >{$}r<{={}$}
    @{}
    >{\raggedright\arraybackslash}X
    @{}
  }%
 }
 {\endtabularx\endminipage\notag}

\begin{document}

\lipsum*[75]
\begin{gather}
x' = \overline{x} \pm u_{\overline{x}} \qquad(P\%)
\\
\begin{where}
\overline{x} & Most probable estimate of $x'$ based on the available data \\
\pm u_{\overline{x}} & Uncertainty interval in that estimate at some probability level, $P\%$ \\
P & Probability level or confidence level
\end{where}
\end{gather}
\lipsum[20]

\end{document}

Answer 2

Here are two possibilities:

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{mathtools}
\usepackage{lipsum} 

\begin{document}

\lipsum[10]
    \begin{flalign}
    & & x' & = \bar{x}\pm u_{\bar{x}}\qquad(P\,\%) & & \\
\shortintertext{where}
 & \begin{aligned}
  \bar{x} & =\rlap{Most probable estimate of $x'$ based on the available data,} \\
  x' & = \rlap{Uncertainty interval at some probability level, \quad$P\,\%$,}\\
  P & = \rlap{Probability level or confidence level. }
\end{aligned}\notag
    \end{flalign}
\lipsum[5]
    \begin{align}
    x' & = \bar{x}\pm u_{\bar{x}}\qquad(P\,\%) \\
\shortintertext{where
  $ \begin{aligned}[t]
  \bar{x} & =\text{Most probable estimate of $x'$ based on the available data,} \\
  x' & = \text{Uncertainty interval at some probability level, \quad$P\,\%$,}\\
  P & = \text{Probability level or confidence level.}
\end{aligned} $} \notag
    \end{align}\mbox{}\vspace*{-2\baselineskip }\par
\lipsum[11]

\end{document}