Align equations with equivalent and equal sign

Question

I am currently trying to get the align environment to work as I want it to work.

\begin{align}
&& a \cdot c + b &= 0\\
\Leftrightarrow && a \cdot c &= -b\\
\end{align}

This code will align the equivalent sign in the middle of the left half and the equal sign in the middle of the right half. What I actually want is that the equivalent sign is on the outer left of the page and the formula is in the middle of the remaining page. How can this be done and is this even encouraged? Or is there a better way to align formula with equivalent and equal signs?

Answer 1

Here are two options:

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{align}
  a \cdot c + b &= 0 \\
  \Leftrightarrow \qquad a \cdot c &= -b
\end{align}

\begin{align}
  a \cdot c + b &= 0 \\
  \llap{$\Leftrightarrow$ \qquad} a \cdot c &= -b
\end{align}

\begin{align}
  a \cdot c + b &= 0 \\
  a \cdot c &= -b \refstepcounter{equation}\tag*{(\theequation)\llap{\makebox[\linewidth][l]{$\Leftrightarrow$}}}
\end{align}
\end{document}

The first sets the \Leftrightarrow a distance of \qquad from the second equation. The second does the same, but removes any influence of \Leftrightarrow in terms of the horizontal spacing. The third sets it as part of the \tag* in order to position it on the left of the text block boundary.

_{The text block boundary is obtained by using the showframe package; not included in the above MWE.}

Answer 2

The first construction I propose below is sometimes used in a blackboard; for a written document, I'd suggest using the natural language and \shortintertext from mathtools:

\documentclass[11pt]{article}
\usepackage{mathtools} 
\usepackage{graphicx}

\begin{document}

\begin{align}
a \cdot c + b &= 0 \\
&\rotatebox[origin=c]{-90}{$\Leftrightarrow$} \notag \\ 
a \cdot c &= -b
\end{align}

\begin{align}
a \cdot c + b &= 0 \\
\shortintertext{if and only if}
a \cdot c &= -b
\end{align}

\end{document}