$$X^2_{i,j} = \sqrt{b^2 - 4ac}$$\[X^2_{i,j} = \sqrt{b^2 - 4ac}\]
\[\sum_{i=1}^{n}\left( \frac{X_i}{Y_i} \right)\]
\[\alpha, \beta, \gamma, \Gamma\]
$$a \pm b$$\[a \pm b\]
$$x \ge 15$$\[x \ge 15\]
$$a_i \ge 0~~~\forall i$$\[a_i \ge 0~~~\forall i\]
$$\int_0^{2\pi} \sin x~dx$$\[\int_0^{2\pi} \sin x~dx\]
$$\begin{array}
{rrr}
1 & 2 & 3 \\
4 & 5 & 6 \\
7 & 8 & 9
\end{array}
$$\[\begin{array} {rrr} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{array} \]
$$\mathbf{X} = \left[\begin{array}
{rrr}
1 & 2 & 3 \\
4 & 5 & 6 \\
7 & 8 & 9
\end{array}\right]
$$\[\mathbf{X} = \left[\begin{array} {rrr} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{array}\right] \]
$$
%% Comment -- define some macros
\def\Xbar{\overline{X}_\bullet}
\def\sumn{\sum_{i=1}^{n}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{align}
\sumn \left(X_i - \Xbar\right) &= \sumn X_i - \sumn \Xbar \\
&= \sumn X_i - n \Xbar \\
&= \sumn X_i - \sumn X_i \\
&= 0
\end{align}
$$\[ %% Comment -- define some macros \def\Xbar{\overline{X}_\bullet} \def\sumn{\sum_{i=1}^{n}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{align} \sumn \left(X_i - \Xbar\right) &= \sumn X_i - \sumn \Xbar \\ &= \sumn X_i - n \Xbar \\ &= \sumn X_i - \sumn X_i \\ &= 0 \end{align} \]
$$
\begin{align}
3+x &=4 && \text{(Solve for} x \text{.)}\\
x &=4-3 && \text{(Subtract 3 from both sides.)}\\
x &=1 && \text{(Yielding the solution.)}
\end{align}
$$``` \[ \begin{align} 3+x &=4 && \text{(Solve for} x \text{.)}\\ x &=4-3 && \text{(Subtract 3 from both sides.)}\\ x &=1 && \text{(Yielding the solution.)} \end{align} \]