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How can I cut the eighteens in the equation like that on the image? What if I also wanted to add a note on the equivalent sign.

enter image description here

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As Óscar says, you can use the cancel package to cross out the numbers, e.g. write \cancel{18}. One way to add a note on the equivalence, modified from the AMS-LaTeX documentation (pp.7-8), is to use the align environment:

\documentclass{article}
\usepackage{cancel}
\usepackage{amsmath}

\begin{document}
    \begin{align*}
        & \Pr\left[Z_{1-\alpha}>\frac{18+\frac{10}{7}-\bar{x}}{\sigma}\right] && \\ 
        \iff  &  \Pr\left[Z_{1-\alpha}>\frac{\cancel{18}+\frac{10}{7}-\cancel{18}}{1.14455}\right] && \text{Explanation}
    \end{align*}
\end{document}

which gives

enter image description here

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