How can I left-align a block of equations that are also horizontally aligned at multiple tabs?

Question

I am trying to display a derivation that should look like:

f(x) = (expression 1) + (expression 2)
                      - (expression 3)

     = (expression 4)

I can get this to display just the way I want, except centered, by using:

\begin{equation*}
\begin{alignedat}{2}
f(x)    &= (\text{expression 1})    &&+ (\text{expression 2}) \\
        &                           &&- (\text{expression 3}) \\ \\
        &= (\text{expression 4})    &&
\end{alignedat}
\end{equation*}

The issue is that if I try any tricks I’ve seen mentioned here on Stack Exchange to left-align equations (such as \flalign), I lose the ability to align my equations relative to each other as desired. I’m fairly new to TeX so might be missing something simple.

Answer 1

If it is for some equations, and not the whole document, the fleqn environment from nccmath does just that:

\documentclass{article}
\usepackage{lipsum}
\usepackage{amsmath, nccmath}

\begin{document}

Some text. Some more text. Some more text. Some more text. Some more text. Some more text. Some more text. Some more text. Some more text. Some more text. Some more text.

\begin{fleqn}
\begin{equation*}
\begin{alignedat}{2}
f(x) &= (\text{expression 1}) &&+ (\text{expression 2}) \\
        & &&- (\text{expression 3}) \\ \\
        &= (\text{expression 4}) &&
\end{alignedat}
\end{equation*}\end{fleqn}

\end{document} 

Answer 2

Since you don't want an equation number, the simplest thing is to use just $...$. BTW, there are no vertical alignments whatsoever in your equation, all alignments are horizontal.

\documentclass{article}
\usepackage{amsmath}
\usepackage{showframe} % just for illustration

\begin{document}

\noindent%
$\displaystyle
\begin{alignedat}{2}
f(x)    &= (\text{expression 1})    &&+ (\text{expression 2}) \\
        &                           &&- (\text{expression 3}) \\ \\
        &= (\text{expression 4})    &&
\end{alignedat}
$

\end{document}