Displaying equation with a line break and all subsequent lines indented

Question

In answering this question, I recommended some changes to the OP and provided the following code:

\documentclass[12pt]{article}
\pagestyle{plain}
\usepackage[margin=1.8cm]{geometry}
\geometry{a4paper}
\usepackage[parfill]{parskip}
\usepackage{amsmath}
\usepackage{amssymb}

\begin{document}

\[
  \begin{aligned}
    |f_{n}&(x)g_{n}(x) - f_{n}(x)g(x) + f_{n}(x)g(x) - f(x)g(x)| \\
    &\leq |f_{n}(x)g_{n}(x) - f_{n}(x)g(x)| + |f_{n}(x)g(x) -
    f(x)g(x)| \\
    &= |f_{n}(x)||g_{n}(x) - g(x)| + |g(x)||f_{n}(x) - f(x)| \\
    &\leq M_{1}\epsilon + M_{2}\epsilon \\
    &= \epsilon(M_1+M_2) \longrightarrow 0 \text{ as } n \to \infty
  \end{aligned}      
\]

\end{document}

Which produces

What I really wanted to do, though, is follow the advice of 3.3.5c of Mathematics Into Type, which recommends breaking at conjunctions and aligning with two-em quad from the left.

That I think is possibly open to interpretation, but what I would like is to have:

|f_{n}&(x)g_{n}(x) - f_{n}(x)g(x) + f_{n}(x)g(x) - f(x)g(x)|

On one line, a line break and all subsequent lines indented by a two-em quad and aligned. In other words, I want what I have, but with a precisely two-em quad indentation:

Unfortunately, the above is the closest I've been able to come. I tried:

\begin{align*}
  |f_{n}(x)g_{n}(x) - f_{n}(x)g(x) + f_{n}(x)g(x) - f(x)g(x)| \\
  \qquad &\leq |f_{n}(x)g_{n}(x) - f_{n}(x)g(x)| + |f_{n}(x)g(x) -
  f(x)g(x)| \\
  &= |f_{n}(x)||g_{n}(x) - g(x)| + |g(x)||f_{n}(x) - f(x)| \\
  &\leq M_{1}\epsilon + M_{2}\epsilon \\
  &= \epsilon(M_1+M_2) \longrightarrow 0 \text{ as } n \to \infty
\end{align*}

But that doesn't work at all:

Answer 1

The mathtools provides the \MoveEqLeft function which achieves exactly what you want. By default, it indents subsequent lines by 2em and it can be further customized with \MoveEqLeft[<number>] which will indent subsequent line by <number> ems:

\documentclass{article}
\usepackage{amsmath}
\usepackage{mathtools}

\begin{document}
\begin{align}
  \MoveEqLeft |f_{n}(x)g_{n}(x) - f_{n}(x)g(x) + f_{n}(x)g(x) - f(x)g(x)| \\
  &\leq |f_{n}(x)g_{n}(x) - f_{n}(x)g(x)| + |f_{n}(x)g(x) - f(x)g(x)| \\
  &= |f_{n}(x)||g_{n}(x) - g(x)| + |g(x)||f_{n}(x) - f(x)| \\
  &\leq M_{1}\epsilon + M_{2}\epsilon \\
  &= \epsilon(M_1+M_2) \longrightarrow 0 \text{ as } n \to \infty
\end{align}      
\begin{align}
  \MoveEqLeft[4] |f_{n}(x)g_{n}(x) - f_{n}(x)g(x) + f_{n}(x)g(x) - f(x)g(x)| \\
  &\leq |f_{n}(x)g_{n}(x) - f_{n}(x)g(x)| + |f_{n}(x)g(x) - f(x)g(x)| \\
  &= |f_{n}(x)||g_{n}(x) - g(x)| + |g(x)||f_{n}(x) - f(x)| \\
  &\leq M_{1}\epsilon + M_{2}\epsilon \\
  &= \epsilon(M_1+M_2) \longrightarrow 0 \text{ as } n \to \infty
\end{align}      
\end{document}

Answer 2

Is this what you want?

\begin{align*}
  &|f_{n}(x)g_{n}(x) - f_{n}(x)g(x) + f_{n}(x)g(x) - f(x)g(x)| \\
  &\qquad \leq |f_{n}(x)g_{n}(x) - f_{n}(x)g(x)| + |f_{n}(x)g(x) - f(x)g(x)| \\
  &\qquad = |f_{n}(x)||g_{n}(x) - g(x)| + |g(x)||f_{n}(x) - f(x)| \\
  &\qquad \leq M_{1}\epsilon + M_{2}\epsilon \\
  &\qquad = \epsilon(M_1+M_2) \longrightarrow 0 \text{ as } n \to \infty
\end{align*}

Answer 3

If you use mathenv of the mdwtools collection, you can use the enhanced {eqnarray} environment. It takes optional column specifiers:

• r, c, l for right-justified, centered, and left-justified math;
• L for left-justified math that is considered to have width 2em;
• and more (read the documentation) so you can completely emulate the functionality of amsmath environments like {align} and others.

Here, you'd use

\documentclass{article}
\usepackage{amstext}
\usepackage{mathenv}

\begin{document}
\begin{eqnarray*}[Ll]
|f_{n}(x)g_{n}(x) - f_{n}(x)g(x) + f_{n}(x)g(x) - f(x)g(x)| \\
&\leq |f_{n}(x)g_{n}(x) - f_{n}(x)g(x)| + |f_{n}(x)g(x) -
f(x)g(x)| \\
&= |f_{n}(x)||g_{n}(x) - g(x)| + |g(x)||f_{n}(x) - f(x)| \\
&\leq M_{1}\epsilon + M_{2}\epsilon \\
&= \epsilon(M_1+M_2) \longrightarrow 0 \text{ as } n \to \infty
\end{eqnarray*}
\end{document}