Vertically center text inside tabularx

Question

In this code, I would like to vertically center the text in the left cells, x = k and x > k. I tried with \parbox[c]:

\documentclass[border=2mm,tikz]{standalone}
\usepackage{tabularx}

\begin{document}

\begin{table}
\renewcommand{\arraystretch}{3}
\begin{tabularx}{0.5\textwidth}{ | X | c | }
\hline
\noindent\parbox[c]{\hsize}{$x = k$} & $a = \displaystyle \frac{1}{2}$\\
& $b = \displaystyle \frac{1}{4}$\\[0.4cm]
\hline
\noindent\parbox[c]{\hsize}{$x > k$} & $c = \displaystyle \frac{1}{8}$\\
 & $d = \displaystyle \frac{1}{16}$\\[0.4cm]
\hline
\end{tabularx}
\end{table}

\end{document}

However, this is the result:

What is wrong? How to vertically center the contents of those cells?

(The use of \parbox is not necessary, I just thought it was a solution).

Answer 1

If you want the left column to be vertically aligned including the added 0.4cm to the row height, then:

\documentclass[border=2mm,tikz]{standalone}
\usepackage{tabularx, multirow, adjustbox}

\begin{document}

\begin{table}
    \renewcommand{\arraystretch}{3}
    \begin{tabularx}{0.5\textwidth}{ | X | c | }
        \hline
        \multirow{2}{*}{\adjustbox{vspace=-0.2cm}{\centerline{$x = k$}}} & $a = \displaystyle \frac{1}{2}$  \\
                                                                         & $b = \displaystyle \frac{1}{4}$  \\[0.4cm]
        \hline
        \multirow{2}{*}{\adjustbox{vspace=-0.2cm}{\centerline{$x > k$}}} & $c = \displaystyle \frac{1}{8}$  \\
                                                                         & $d = \displaystyle \frac{1}{16}$ \\[0.4cm]
        \hline
    \end{tabularx}
\end{table}

\end{document}

If the 0.4cm is removed, then you can simply remove the \adjustbox{vspace-0.2cm}{} command. Also, the measurement can be adjusted if you change the value of the added row height.

Answer 2

Here is an alternative without multirow but with nested tabulars and makecell:

\documentclass{article}
\usepackage{tabularx}
\usepackage{makecell}
\setcellgapes{0.25cm}

\begin{document}

\begin{table}
\makegapedcells
    \begin{tabularx}{0.5\textwidth}{ | >{\centering\arraybackslash}X | c | }
        \hline
        $x = k$ & \begin{tabular}{>{\(\displaystyle}c<{\)}} a = \frac{1}{2} \\ b = \frac{1}{4} \end{tabular}\\
        \hline
        $x > k$ & \begin{tabular}{>{\(\displaystyle}c<{\)}} c = \frac{1}{8} \\ d = \frac{1}{16} \end{tabular}\\
        \hline
    \end{tabularx}
\end{table}

\end{document}