How to justify steps (e.g., citing numbered equations) in a displayed chain of equations

Question

I have a chain of equations in AMS align environment in LyX, and I want to cite numbered equations as justification for some of my steps in the chain (see the picture).

I don't know if there's a standard way to do this. My current method is to introduce horizontal space and then to cite the reasoning to the right. However, when I do this the displayed chain is pushed to the left (hence no longer centered) and the amount of horizontal spacing needed changes dramatically. Is there a uniform way to justify steps on the right of the chain while keeping the chain centered? If there's a more standard way to justify steps in a chain, I'm open to suggestions. Thanks in advance.

MWE:

\documentclass[english,reqno]{amsart}
\usepackage[T1]{fontenc}
\usepackage[latin9]{inputenc}
\usepackage{amstext}
\usepackage{amsthm}
\usepackage{setspace}

\makeatletter
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Textclass specific LaTeX commands.
\numberwithin{figure}{section}

\makeatother

\usepackage{babel}
\begin{document}
\begin{singlespace}
\begin{align*}
A= & B\\
= & C\qquad\qquad\text{by \ensuremath{\left(3\right)}}
\end{align*}
\end{singlespace}

Answer 1

In LyX, enter display math mode (Ctrl+Shift+M), and then right click on the region to select AMS align environment. You'll see

At the bottom of the screen, you should see

Click on the circled icon to add a column to the right. You can then write your justification in that third column as in

Note that this will right-aligned the justifications

If you want the justifications to be left-aligned, simply add a fourth column, and write your justifications there (and leave the third one blank).

The output will be

Answer 2

Every other & is assumed to start a new equation, so will have a much larger gap. It doesn't look so bad if the equation is longer.

\documentclass[english,reqno]{amsart}
\usepackage[T1]{fontenc}
\usepackage[latin9]{inputenc}
\usepackage{amstext}
\usepackage{amsthm}
\usepackage{setspace}

\makeatletter
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Textclass specific LaTeX commands.
\numberwithin{figure}{section}

\makeatother

\usepackage{babel}
\begin{document}
\begin{singlespace}
\begin{align*}
A &= B\\
 &= C  &&\text{by \ensuremath{\left(3\right)}}
\end{align*}
\end{singlespace}
\end{document}

Answer 3

Try the alignat environment from AMSmath.

For example:

\documentclass{article}
\usepackage{amsmath}
\begin{document}

\begin{alignat*}{2}
     A=&B && \\
    =&C&&\textrm{ by (3)}\\
    \hphantom{\textrm{ by (6)}}\hspace{1cm}=&\sqrt{\frac{D+D^2}{E}}\hspace{1cm}&&\textrm{ by (6)}
\end{alignat*}

\end{document}

You can make any number of aligned columns, aligned right where the last one left off. If you want to reposition, just add horizontal space (or negative horizontal space) right after the single longest line on the previous column. To center the first column, simply place horizontal space before the first alignment tab equal to the space before and after the second alignment tab.

Credit: Multiple alignment -- I didn't even know how to answer this question when I saw it. I just got lucky browsing stackexchange on an unrelated matter.

Another centering option: if you are worried about centering something complicated, you can use \textrm{\put(x,y){text}} on each justification, with y=0 and x an appropriate positive size (experiment). This will push them off to the right and keep the main equation centered. In that case, alignat isn't actually necessary.