I would not use the equation environment; rather, I would use flalign as such:
(notice the && at the end of each line)
\documentclass{article}
\usepackage{amsmath}
\begin{document}
\noindent A \hfill Z
\begin{flalign}
a_{ijk} &= \frac {Pr(M_{I} =2 \& M_J=1 \& M_K =1 | I=i , J=j , K=k)}{Pr (M_I =1 \& M_J =1 \& M_K=1 | I=i , J=j)}&&\\\nonumber
&= \frac {\mu_{ijk211}}{\mu_{ijk111}}&&
\end{flalign}
\noindent A \hfill Z
\end{document}
![Output](https://i.stack.imgur.com/ObrGK.png)
Another way to go is to set the fleqn
option for the document class. However, this left-aligns all of your equations and hence should not be used when you want at least some equations to remain centered.
\documentclass[fleqn]{article}
\usepackage{amsmath}
\begin{document}
\noindent A \hfill Z
\begin{equation}
\begin{aligned}
a_{ijk} &= \frac {Pr(M_{I} =2 \& M_J=1 \& M_K =1 | I=i , J=j , K=k)}{Pr (M_I =1 \& M_J =1 \& M_K=1 | I=i , J=j)}\\
&= \frac {\mu_{ijk211}}{\mu_{ijk111}}\\
\end{aligned}
\end{equation}
\noindent A \hfill Z
\end{document}
For this output:
![Output 2](https://i.stack.imgur.com/9MCxp.png)
As suggested by karlkoeller, if you want to get rid of the space between the left margin and the equation (to get a result similar to the first case), you should add \setlength{\mathindent}{0pt}
.
If you later want to indent it back to its default value, you can use the same command with a value of 15pt
, which is the amount of pt
a paragraph indent shifts its text to the right.
I find no reason for this display to be flush left. Anyway…
\documentclass{article}
\usepackage{amsmath}
\begin{document}
The following display is left aligned. I don't know why it should be
treated differently from the other displays, but here it is anyhow.
\begin{flushleft}
$\begin{aligned}
a &=(3+6+9+12+\dots+147)+1125\\
&=3 \cdot (1+2+3+4+\dots+49)+1125\\
&=3 \cdot \frac{49 \cdot 50}{2} + 1125=49 \cdot 75 + 1125\\
&=3675 + 1125\\
&=4900\\
&=70^2 \Rightarrow \sqrt{a} = \sqrt{70^2}=70
\end{aligned}$
\end{flushleft}
Note that dots should be specified with \verb|\dots|, not with
three periods and that \verb|\displaystyle| is not needed; there
is \verb|\dfrac|, if needed (not here).
\end{document}
![enter image description here](https://i.stack.imgur.com/PL0SH.png)
Best Answer
It really depends on what you mean by left alignment of a single equation. Here are some options: