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I have another idea, maybe split will be suitable for you. \documentclass{article} \usepackage{amsmath} \begin{document} $$\left\{ \begin{split} \Delta l &= \Delta l_1 + \Delta l_2\\ N &= N_1(\Delta l_1)=N_2(\Delta_2)\\ \end{split}\right.$$ \end{document}

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One can have a slightly simpler syntax with the empheq package (which loads mmathtools, hence amsmath): \documentclass{article} \usepackage[overload]{empheq} \begin{document} [left=\empheqlbrace] \!\begin{aligned} Δ l &= Δ l_1 + Δ l_2\\ N &= N_1(Δ l_1)=N_2(Δ_2) \end{aligned} \end{document} ...

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I suggest using \makebox and \raisebox. The top diagram can be set in a box as wide as the requested displacement, the bottom one moved down by 1em (the size of a square) plus the displacement. \documentclass[12pt]{article} \usepackage{amsmath} \usepackage{ytableau} \usepackag-e{calc} \begin{document} \ytableausetup{boxsize=1em} ...

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Here are the options you have rewording the sentence adding \allowbreak at appropriate points in the formula, e.g. P(x,\allowbreak y,\allowbreak z) = q displaying the equation without a number using the package microtype to give more flexibility to spacing in the paragraph increasing \emergencystretch for the paraagraph: {\emergencystretch=1.5em .... \par} ...

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The matrix environments of the amsmath package have to be set in math mode. You didn't do that, thus TeX is searching for some $which enables this math mode. If you put it in$$$...$$\$, $$$$...$$$$, $$$...$$$, \begin{displaymath}$$...$$\end{displaymath}, $$...$$ or \begin{equation*}$$...$$\end{equation*}, (and most certainly others$$...$$,) it will $$...$$

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