How to make a big equation fit in a single slide?
I have the following equation:
\begin{frame}
\begin{equation}
\begin{split}
(\lambda_1-2n+l+4)(\lambda_1-n-l+2)\leq l(n-l)
\\
\implies \lambda_1^2+\lambda_1(6-3n)+(2n^2-2l-8n+8)\leq 0
\\
\implies \bigg \{ 2\lambda_1-\bigg(3n-6-\sqrt{8l+n^2-4n+4}\bigg )\bigg \}\bigg \{ 2\lambda_1-\bigg(3n-6+\sqrt{8l+n^2-4n+4}\bigg)\bigg \} \leq 0
\\
\implies \frac{3n-6-\sqrt{8l+n^2-4n+4}}{2}\leq \lambda_1 \leq \frac{3n-6+\sqrt{8l+n^2-4n+4}}{2}
\end{split}
\end{equation}
\end{frame}
Whenever I am using \begin{frame}
\end{frame}
a part of my equation is going outside the frame.
How can I adjust the whole equation in a single slide?
Please help me out.
Best Answer
Here's a solution suggestion that performs alignment on the inequality symbols.
Aside: The
\bigg
sizing instructions are, in my opinion, excessive;\big
and\Big
suffice completely.Addendum: Here's a second solution, inspired by @egreg's observation that a lot of space is taken up by the repeated term
\sqrt{8l+n^2-4n+4}
. Replacing it with the symbolD
, rewriting the final row to use interval notation instead of a pair of inequalities, and aligning the rows on the\implies
symbols instead of on the inequality symbols yields the following result: