The following LaTeX code was saved in ~/Test.tex.
\documentclass{article}
%\usepackage[bidi=basic,hebrew,provide=*]{babel}
%\babelfont{rm}[Renderer=HarfBuzz]{FreeSans}
\usepackage{amsmath}
\usepackage{aliascnt}
\newaliascnt{inequality}{equation}
\aliascntresetthe{inequality}
\makeatletter
\def\inequality{$$\refstepcounter{inequality}}
\def\endinequality{\eqno\hbox{@eqnnum}$$@ignoretrue}
\makeatother
\begin{document}
\begin{equation}\label{eq}
1=1
\end{equation}
\begin{inequality}\label{ineq}
1\neq2
\end{inequality}
\end{document}
The code uses the method described in this answer to create a new equation-like environment called inequality, whose counter is aliased to the counter of the equation environment. This trick is intended to be used in conjunction with cleveref cross-references, but for the purposes of this question cross-referencing is redudant, and therefore was not exercised in the MWE above.
Then the following commands were executed in the Terminal:
> cd ~
> lualatex Test
Consequently a PDF file was generated at ~/Test.pdf. When opened in a PDF viewer, the file displayed as follows. (I screenshot only the relevant part of the display.)
As can be seen, the numbers of both the equation and the inequality appear on the right side of the text region.
The two commented LaTeX lines were now uncommented to establish Hebrew as the document's main language, and the code was recompiled. The resulting PDF file looked as follows.
As can be seen, the number of the inequality switched sides and is now left-aligned, whereas the number of the equality remains right-aligned.
This behavior is undesirable. The inequality's number should be right-aligned to match the alignment of the equality's number. How can this be accomplished?



\leqnonot\eqno– David Carlisle Dec 05 '22 at 16:03\align. – Evan Aad Dec 05 '22 at 16:04leqnoclass option, the inequality's number vanishes. – Evan Aad Dec 05 '22 at 16:05\leqnoproduces what you ask for (produced with\leqnoafter uncommenting the babel lines) Obviously as you have chosen to use tex primitives such as$$and\eqnoyou need to be responsble for switching sides, you can not expect babel to do it – David Carlisle Dec 05 '22 at 16:09