Arranging equation after leftrightarrow sign

Question

How to arrange the equation after Leftrightarrow sign?

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage{amsfonts}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{float}
\usepackage{graphics}
\begin{document}
\begin{equation}
    \begin{aligned}
        & \Leftrightarrow - \scalebox{0.975}{$\biggl(\left(\alpha + \mu + \rho\right)\left(\left( a_1 + \left( \alpha + \mu\right)\right)^2 + a_1 a_2\right) + \left( a_1 + \left(\alpha + \mu\right)\right)\gamma \rho \biggr)$} > 0 \
        & \Leftrightarrow \left(\alpha + \mu + \rho\right)\left(\left( a_1 + \left( \alpha + \mu\right)\right)^2 + a_1 a_2\right) + \left( a_1 + \left(\alpha + \mu\right)\right)\gamma \rho < 0 \
        & \Leftrightarrow \scalebox{0.875}{$\left(\alpha + \mu + \rho\right)\left(\left(\frac{\Lambda\beta \left(\alpha+\mu+\rho\right)}{\left(\alpha+ \mu\right)\left(\alpha + \mu + \gamma + \rho\right)}\right)^2 + \Lambda \beta - \frac{\left(\alpha+ \mu\right)^2\left(\alpha + \mu + \gamma + \rho\right)}{\alpha+\mu+\rho}\right) + \left(\frac{\Lambda\beta \left(\alpha+\mu+\rho\right)}{\left(\alpha+ \mu\right)\left(\alpha + \mu + \gamma + \rho\right)}\right)\gamma \rho$} < 0 \
        & \Leftrightarrow \scalebox{0.85}{$\left(\alpha + \mu + \rho\right)\left(\frac{\Lambda\beta \left(\alpha+\mu+\rho\right)}{\left(\alpha+ \mu\right)\left(\alpha + \mu + \gamma + \rho\right)}\right)^2+ \Lambda \beta\left(\alpha + \mu + \rho\right) - \left(\alpha+ \mu\right)^2\left(\alpha + \mu + \gamma + \rho\right) $} \
        & \scalebox{0.9}{$ + \left(\frac{\Lambda\beta \left(\alpha+\mu+\rho\right)}{\left(\alpha+ \mu\right)\left(\alpha + \mu + \gamma + \rho\right)}\right)\gamma \rho $} < 0 \
        & \Leftrightarrow \scalebox{0.9}{$\left(\alpha+ \mu\right)^2\left(\alpha + \mu + \gamma + \rho\right)$} > \
        & \scalebox{0.9}{$\left(\alpha + \mu + \rho\right)\left(\frac{\Lambda\beta \left(\alpha+\mu+\rho\right)}{\left(\alpha+ \mu\right)\left(\alpha + \mu + \gamma + \rho\right)}\right)^2+ \Lambda \beta\left(\alpha + \mu + \rho\right) + \left(\frac{\Lambda\beta \left(\alpha+\mu+\rho\right)}{\left(\alpha+ \mu\right)\left(\alpha + \mu + \gamma + \rho\right)}\right)\gamma \rho$} \
    \end{aligned}
\end{equation}
\end{document}

I'd suggest, in the lines that begin with \Leftrightarrow, move the & after the \Leftrightarrow. Leave it where it is in the other lines. But there are other (better) ways to get smaller type than using \scalebox; I believe there's another question dealing with that, but it may take a while to find it. — barbara beeton, Jan 09 '22 at 03:32
Here is a question that addresses the matter of "smallifying" a display: Use of \small to resize a math display affects the baseline stretch of the preceding paragraph — barbara beeton, Jan 09 '22 at 03:43
What's with the excessive use of \left and \right for every single parenthesis? I can count more than 50 [!] instances each of \left and \right... — Mico, Jan 09 '22 at 06:04

score 1 · Answer 1 · answered Jan 09 '22 at 05:34

You may use the IEEEeqnarray environment from the IEEEtrantools package for nice alignment.

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage{amsfonts}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{IEEEtrantools}
\usepackage{float}
\usepackage{graphics}
\usepackage{showframe}
\begin{document}
Using \verb|\IEEEeqnarray| with \verb|\scalebox|
\begin{IEEEeqnarray}{rCl}
        & \Leftrightarrow & - \scalebox{0.975}{$\biggl(\left(\alpha + \mu + \rho\right)\left(\left( a_1 + \left( \alpha + \mu\right)\right)^2 + a_1 a_2\right) + \left( a_1 + \left(\alpha + \mu\right)\right)\gamma \rho \biggr)$} > 0 \
        & \Leftrightarrow & \left(\alpha + \mu + \rho\right)\left(\left( a_1 + \left( \alpha + \mu\right)\right)^2 + a_1 a_2\right) + \left( a_1 + \left(\alpha + \mu\right)\right)\gamma \rho < 0 \
        & \Leftrightarrow & \scalebox{0.875}{$\left(\alpha + \mu + \rho\right)\left(\left(\frac{\Lambda\beta \left(\alpha+\mu+\rho\right)}{\left(\alpha+ \mu\right)\left(\alpha + \mu + \gamma + \rho\right)}\right)^2 + \Lambda \beta - \frac{\left(\alpha+ \mu\right)^2\left(\alpha + \mu + \gamma + \rho\right)}{\alpha+\mu+\rho}\right) + \left(\frac{\Lambda\beta \left(\alpha+\mu+\rho\right)}{\left(\alpha+ \mu\right)\left(\alpha + \mu + \gamma + \rho\right)}\right)\gamma \rho$} < 0 \
        & \Leftrightarrow & \scalebox{0.85}{$\left(\alpha + \mu + \rho\right)\left(\frac{\Lambda\beta \left(\alpha+\mu+\rho\right)}{\left(\alpha+ \mu\right)\left(\alpha + \mu + \gamma + \rho\right)}\right)^2+ \Lambda \beta\left(\alpha + \mu + \rho\right) - \left(\alpha+ \mu\right)^2\left(\alpha + \mu + \gamma + \rho\right) $} \
        & & \scalebox{0.9}{$ + \left(\frac{\Lambda\beta \left(\alpha+\mu+\rho\right)}{\left(\alpha+ \mu\right)\left(\alpha + \mu + \gamma + \rho\right)}\right)\gamma \rho $} < 0 \
        & \Leftrightarrow & \scalebox{0.9}{$\left(\alpha+ \mu\right)^2\left(\alpha + \mu + \gamma + \rho\right)$} > \
        & & \scalebox{0.9}{$\left(\alpha + \mu + \rho\right)\left(\frac{\Lambda\beta \left(\alpha+\mu+\rho\right)}{\left(\alpha+ \mu\right)\left(\alpha + \mu + \gamma + \rho\right)}\right)^2+ \Lambda \beta\left(\alpha + \mu + \rho\right) + \left(\frac{\Lambda\beta \left(\alpha+\mu+\rho\right)}{\left(\alpha+ \mu\right)\left(\alpha + \mu + \gamma + \rho\right)}\right)\gamma \rho$} \
\end{IEEEeqnarray}
Using \verb|\IEEEeqnarray| with \verb|\footnotesize|
{\footnotesize
\begin{IEEEeqnarray}{rCl}
        & \Leftrightarrow & - \biggl(\left(\alpha + \mu + \rho\right)\left(\left( a_1 + \left( \alpha + \mu\right)\right)^2 + a_1 a_2\right) + \left( a_1 + \left(\alpha + \mu\right)\right)\gamma \rho \biggr) > 0 \
        & \Leftrightarrow & \left(\alpha + \mu + \rho\right)\left(\left( a_1 + \left( \alpha + \mu\right)\right)^2 + a_1 a_2\right) + \left( a_1 + \left(\alpha + \mu\right)\right)\gamma \rho < 0 \
        & \Leftrightarrow & \left(\alpha + \mu + \rho\right)\left(\left(\frac{\Lambda\beta \left(\alpha+\mu+\rho\right)}{\left(\alpha+ \mu\right)\left(\alpha + \mu + \gamma + \rho\right)}\right)^2 + \Lambda \beta - \frac{\left(\alpha+ \mu\right)^2\left(\alpha + \mu + \gamma + \rho\right)}{\alpha+\mu+\rho}\right) \
        & & \negmedspace {} + \left(\frac{\Lambda\beta \left(\alpha+\mu+\rho\right)}{\left(\alpha+ \mu\right)\left(\alpha + \mu + \gamma + \rho\right)}\right)\gamma \rho < 0 \
        & \Leftrightarrow & \left(\alpha + \mu + \rho\right)\left(\frac{\Lambda\beta \left(\alpha+\mu+\rho\right)}{\left(\alpha+ \mu\right)\left(\alpha + \mu + \gamma + \rho\right)}\right)^2+ \Lambda \beta\left(\alpha + \mu + \rho\right) - \left(\alpha+ \mu\right)^2\left(\alpha + \mu + \gamma + \rho\right)  \
        & & \negmedspace {} + \left(\frac{\Lambda\beta \left(\alpha+\mu+\rho\right)}{\left(\alpha+ \mu\right)\left(\alpha + \mu + \gamma + \rho\right)}\right)\gamma \rho  < 0 \
        & \Leftrightarrow & \left(\alpha+ \mu\right)^2\left(\alpha + \mu + \gamma + \rho\right) > \left(\alpha + \mu + \rho\right)\left(\frac{\Lambda\beta \left(\alpha+\mu+\rho\right)}{\left(\alpha+ \mu\right)\left(\alpha + \mu + \gamma + \rho\right)}\right)^2\
        & & \negmedspace {} + \Lambda \beta\left(\alpha + \mu + \rho\right) + \left(\frac{\Lambda\beta \left(\alpha+\mu+\rho\right)}{\left(\alpha+ \mu\right)\left(\alpha + \mu + \gamma + \rho\right)}\right)\gamma \rho \
\end{IEEEeqnarray}}
\end{document}

Note: You may read Is it ever bad to use \left and \right?. Also, it is discouraged to scale elements that contains text.

Okay, it works on me. Thank you. – pagesays404 Jan 09 '22 at 05:48 — pagesays404, Jan 09 '22 at 05:48

score 0 · Answer 2 · answered Jan 09 '22 at 06:35

I would like to strongly recommend that you not use \adustbox anywhere in this math expression. Just insert a couple more line breaks by hand, if and when needed.

I would also use an align* environment instead of a nested equation*/aligned setup.

A separate observation: It may be a cathartic experience for you not to use \left and \right on every single parenthesis. I can count over 50 [!] instances each of these two autosizing directives. With some fairly easy analysis, the number can be brought down to 9 [yes, just nine] pairs of "big" parentheses. And, instead of using round parentheses exclusively, do also consider using square brackets (or curly braces...) from time to time to provide some simple yet very effective visual clues.

\documentclass{article}
%\usepackage[utf8]{inputenc} % that's the default nowadays
\usepackage[T1]{fontenc}
\usepackage{amsmath,amssymb}
\begin{document}
\begin{align*}
  &\Leftrightarrow -\bigl[
    (\alpha + \mu + \rho)\bigl(( a_1 + ( \alpha + \mu))^2 + a_1 a_2\bigr) 
    + \bigl( a_1 + (\alpha + \mu)\bigr)\gamma \rho \bigr] > 0 \
  &\Leftrightarrow 
   (\alpha + \mu + \rho)\bigl(( a_1 + ( \alpha + \mu))^2 + a_1 a_2\bigr) 
    + \bigl( a_1 + (\alpha + \mu)\bigr)\gamma \rho < 0 \
  &\Leftrightarrow 
   (\alpha + \mu + \rho)\biggl[\biggl(\frac{\Lambda\beta (\alpha+\mu+\rho)}{(\alpha+ \mu)(\alpha + \mu + \gamma + \rho)}\biggr)^{!!2} + \Lambda \beta

\frac{(\alpha+ \mu)^2(\alpha + \mu + \gamma + \rho)}{\alpha+\mu+\rho}\biggr] \

&\qquad + \frac{\Lambda\beta (\alpha+\mu+\rho)}{(\alpha+ \mu)(\alpha + \mu + \gamma + \rho)},\gamma \rho < 0 \
  &\Leftrightarrow (\alpha + \mu + \rho)
   \biggl(\frac{\Lambda\beta (\alpha+\mu+\rho)}{(\alpha+ \mu)(\alpha + \mu + \gamma + \rho)}\biggr)^{!!2}

\Lambda \beta(\alpha + \mu + \rho) \

&\qquad - (\alpha+ \mu)^2(\alpha + \mu + \gamma + \rho)

\frac{\Lambda\beta (\alpha+\mu+\rho)}{(\alpha+ \mu)(\alpha + \mu + \gamma + \rho)},\gamma \rho  < 0 \

&\Leftrightarrow (\alpha+ \mu)^2(\alpha + \mu + \gamma + \rho) >{} \
  &\qquad (\alpha + \mu + \rho)\biggl(\frac{\Lambda\beta (\alpha+\mu+\rho)}{(\alpha+ \mu)(\alpha + \mu + \gamma + \rho)}\biggr)^{!!2}

\Lambda \beta(\alpha + \mu + \rho) \

&\qquad\quad

\frac{\Lambda\beta (\alpha+\mu+\rho)}{(\alpha+ \mu)(\alpha + \mu + \gamma + \rho)},\gamma \rho

\end{align*}
\end{document}

score 0 · Answer 3 · answered Jan 09 '22 at 07:55

With use of the multlined defined in the mathtools package, without scaling parts of equation systems and manuals settings of parenthesis sizes:

\documentclass{article}
\usepackage{mathtools}
%--------------- show page layout. don't use in a real document!
\usepackage{showframe}
\renewcommand\ShowFrameLinethickness{0.15pt}
\renewcommand*\ShowFrameColor{\color{red}}
%---------------------------------------------------------------%
\begin{document}
[
    \begin{aligned}
\Leftrightarrow 
    & - \biggl((\alpha + \mu + \rho) \bigl((a_1 + \alpha + \mu)^2 + a_1 a_2\bigr) + ( a_1 + \alpha + \mu)\gamma \rho \biggr) > 0 \
\Leftrightarrow {}
    & (\alpha + \mu + \rho)\bigl(( a_1 + \alpha + \mu)^2 + a_1 a_2\bigr) + (a_1 + \alpha + \mu)\gamma \rho < 0 \
\Leftrightarrow {}
    & \begin{multlined}[t]
        (\alpha + \mu + \rho)
        \Biggl(\biggl(\frac{\Lambda\beta (\alpha+\mu+\rho)}{(\alpha+ \mu)(\alpha + \mu + \gamma + \rho)}
               \biggr)^2    \
        + \Lambda \beta - \frac{(\alpha+ \mu)^2 (\alpha + \mu + \gamma + \rho)}{\alpha+\mu+\rho}\Biggr)
         + \biggl(\frac{\Lambda\beta \left(\alpha+\mu+\rho\right)}{\left(\alpha+ \mu\right)\left(\alpha + \mu + \gamma + \rho\right)}\biggr)\gamma \rho  < 0
     \end{multlined}\
\Leftrightarrow {}
    & \begin{multlined}[t]
        (\alpha + \mu + \rho)
        \biggl(\frac{\Lambda\beta (\alpha+\mu+\rho)}{(\alpha+ \mu)(\alpha + \mu + \gamma + \rho)}\biggr)^2
        + \Lambda \beta (\alpha + \mu + \rho )     \
        -  (\alpha+ \mu)^2 (\alpha + \mu + \gamma + \rho)
        + \biggl(\frac{\Lambda\beta (\alpha+\mu+\rho )}{(\alpha+ \mu) (\alpha + \mu + \gamma + \rho)}\biggr)\gamma \rho < 0

     \end{multlined}    \
\Leftrightarrow {}
    & \begin{multlined}[t]
        (\alpha+ \mu)^2 (\alpha + \mu + \gamma + \rho) >    \
        (\alpha + \mu + \rho)
        \biggl(\frac{\Lambda\beta (\alpha+\mu+\rho)}{(\alpha+ \mu)
        (\alpha + \mu + \gamma + \rho)}\biggr)^2            \
        +  \Lambda \beta(\alpha + \mu + \rho) + 
        \biggl(\frac{\Lambda\beta (\alpha+\mu+\rho)}{(\alpha+ \mu)(\alpha + \mu + \gamma + \rho)}\biggr)\gamma \rho
     \end{multlined}
    \end{aligned}
]
\end{document}

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Arranging equation after leftrightarrow sign

3 Answers3