Print basic calculations step by step

Question

I would like to achieve two goals with the code below.

1. Change the width of the red rectangle.
2. Draw the arrows added by hand in the following screenshot.

Any clue or advice will be appreciated.

\documentclass{article}

\usepackage{nicematrix}
\usepackage{tikz}

\begin{document}

$\begin{NiceArray}{rcl}[name=test]
    2 x + 3 & = & 5 x - 4
    \\[-.5em]
    \\
    \Block[draw=red]{1-3}{- 3}
    \\
    \\[-.5em]
        2 x & = & 5 x - 7
    \\[-.5em]
    \\
    \Block[draw=red]{1-3}{- 5x}
    \\
    \\[-.5em]
        -3 x & = & - 7
\end{NiceArray}$

\end{document}

Answer 1

Here is an automatic method.

\documentclass{article}

\usepackage{nicematrix,tikz}
\usetikzlibrary{calc}

\ExplSyntaxOn
\cs_new_protected:Nn \__projetmbc_ii:n
  {
    \begin{tikzpicture}
    \draw [->] ($(#1-|2)+(-1mm,4pt)$) -- ($(\int_eval:n { #1 + 1 } -| 2)+(-1mm,-4pt)$) ;
    \draw [->] ($(#1-|3)+(1mm,4pt)$) -- ($(\int_eval:n { #1 + 1 } -| 3)+(1mm,-4pt)$) ;
    \end{tikzpicture}
  }

\cs_new_protected:Nn \__projetmbc_i:n
  {
    \tl_gput_right:Nx \g_nicematrix_code_before_tl
      { \__projetmbc_ii:n { \arabic { iRow } } }
    \Block[draw=red,fill=white]{1-3}{#1}
  }

\NewExpandableDocumentCommand \NewLineWithBox { m }
  { \\[1mm] \__projetmbc_i:n {#1} \\ \noalign{\vspace{2mm}} }

\ExplSyntaxOff

\begin{document}

\NiceMatrixOptions{cell-space-limits=2pt}

$\begin{NiceArray}{r@{}>{{}}c<{{}}@{}l}
2x+3 & = & 5x-4 \NewLineWithBox{-3}
 2x  & = & 5x-7 \NewLineWithBox{-5x}
-3 x & = & - 7  \NewLineWithBox{\text{\Huge Huge}}
-3 x & = & - 7
\end{NiceArray}$

\end{document}

You need several compilations (because nicematrix uses PGF/Tikz nodes).

Answer 2

Here is a solution.

 \documentclass{article}

 \usepackage{nicematrix,tikz}
 \usetikzlibrary{calc}

 \begin{document}

 $\begin{NiceArray}{r@{}c@{}l}
 2x+3 & {} = {} & 5x-4 \\[7mm]
  2x  & {} = {} & 5x-7 \\
 \CodeAfter
 \begin{tikzpicture}
 \draw [->,shorten < = 1pt, shorten > = 1pt]
       let \p1 = ([xshift=-1mm]1-1.south east) ,
           \p2 = (2-1.north) 
       in (\p1) -- (\x1,\y2) ;
 \draw [->,shorten < = 1pt, shorten > = 1pt]
       let \p1 = ([xshift=1mm]1-3.south west) ,
           \p2 = (2-3.north) 
       in (\p1) -- (\x1,\y2) ;
 \node [draw, fill=white] at ([yshift=-5mm]1-2){\;$-3$\;} ;
 \end{tikzpicture}
 \end{NiceArray}$

 \end{document}

You need several compilations (because nicematrix uses PGF/Tikz nodes).