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How do I align the \Rightarrow commands of these separate equations? Please note that the \hspace{7.5cm} commands of the second equation are my attempt at manual adjustment. Also, I know that there are many other queries like this one, but the issue I have with the answers is that they suggested placing both equations in one \align environment and then using \intertext. But this doesn't really work in my case, since I would like to keep the "if" statements on the left margin, just like regular text.

If $\delta = \cfrac{1}{\mid l \mid + 1}$
\begin{alignat*}{3}
&\Rightarrow \ \mid x \mid \ < \ \cfrac{1}{\mid l \mid + 1} \hspace{4cm} &&\text{true statement, as $\delta>0$} \\
&\Rightarrow \ \mid l \mid + 1 \ < \ \mid \cfrac{1}{x} \mid \hspace{4cm} &&\text{t.s.}
\end{alignat*}

If $\epsilon = 1$
\begin{equation*}
\begin{split}
&\Rightarrow \ \mid \frac{1}{x} - l \mid \ < \ 1 \hspace{7.5cm}\\
&\Rightarrow \ \mid \frac{1}{x} \mid \ < \ 1 + \mid l \mid \hspace{7.5cm}
\end{split}
\end{equation*}
\hfill a false statement, since it contradicts a true statement

Thanks!

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  • Unrelated: you have a misuse of alignat*{3}: 3 & mean you have two alignment columns, not three. More generally, n alignment points require 2n – 1 ampersands.
    – Bernard
    Nov 19, 2018 at 20:29

2 Answers 2

4

I'm not sure what you mean, because with \intertext the text goes at the left margin.

\documentclass{article}
\usepackage{amsmath}

\begin{document}

If $\delta = \dfrac{1}{\lvert l\rvert + 1}$
\begin{align*}
&\Rightarrow\quad \lvert x \rvert < \frac{1}{\lvert l \rvert + 1} &&\text{true statement, as $\delta>0$} \\
&\Rightarrow \quad \lvert l \rvert + 1 < \Bigl\lvert \frac{1}{x} \Bigr\rvert &&\text{true statement} \\
\intertext{If $\epsilon = 1$}
&\Rightarrow \quad \Bigl\lvert \frac{1}{x} - l \Bigr\rvert < 1 \\
&\Rightarrow \quad \Bigl\lvert \frac{1}{x} \Bigr\rvert < 1 + \lvert l \rvert
\end{align*}
a false statement, since it contradicts a true statement

\end{document}

enter image description here

Note that \mid is not for the absolute value; also \ <\ adds too much space around the relation symbol.

1

In this particular case, using \intertext{} is the way to go.

However, if you insist on doing it with two separate align environments, you need to insert appropriate \hphantom{} spacing. Here, it was only necessary to add the \hphantom{} to the first equation in the second align. In most cases it won't be as simple as this ended up being.

enter image description here

Code:

\documentclass{article}
\usepackage{amsmath}

\newcommand*{\WidestText}{\text{true statement, as $\delta>0$}}

\begin{document}

If $\delta = \dfrac{1}{\lvert l\rvert + 1}$
\begin{align*}
    &\Rightarrow\quad \lvert x \rvert < \frac{1}{\lvert l \rvert + 1} 
        &&\WidestText 
    \\
    &\Rightarrow \quad \lvert l \rvert + 1 < \Bigl\lvert \frac{1}{x} \Bigr\rvert 
        &&\text{true statement}
\end{align*}
If $\epsilon = 1$
\begin{align*}
    &\Rightarrow \quad \Bigl\lvert \frac{1}{x} - l \Bigr\rvert < 1 && \hphantom{\WidestText} \\
    &\Rightarrow \quad \Bigl\lvert \frac{1}{x} \Bigr\rvert < 1 + \lvert l \rvert
\end{align*}
a false statement, since it contradicts a true statement.
\end{document}

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