\documentclass{article}
\usepackage{mathtools}
\usepackage{amsmath}
\usepackage{amssymb}
\begin{document}

\[
  1+1
      \]

\begin{align}
    2+2 = 4\\[1ex]
        3+3 = 6
    \end{align}

\begin{equation}
   \left(
     f(x) = 3
  \right)
  \left.
      f(x) = 3
\right.
\end{equation}

Test $[ ... )$ of unmatched brackets in
inline math text.

In R, there is the operator \verb|[<-|...
that ...

\begin{equation*} 
  \left \{ 
    \begin{aligned}
      -\Delta \theta &= u \quad \text{in } \Omega, \\
      \theta &=0 \quad \text{on } \Gamma.
    \end{aligned}
  \right.
\end{equation*}

\begin{equation} \label{eq:state2}
  \left\{
    \begin{aligned}
      -\div [a_M(z)\nabla y + b(\nabla y)]  &= u \quad \text{in } \Omega, \\
      y &=0 \quad \text{on } \Gamma.
    \end{aligned}
  \right.
\end{equation}

\begin{equation}
    \left\{
        \begin{aligned}
            \min_{u,y} &J(u,y) \\
            \text{s.t.} \quad
            &
                -\Delta y = u \text{in } \Omega\\
                y = 0 \text{on } \partial\Omega.
             \\
            &\begin{aligned}[t]
                -\Delta y &= u && \text{in } \Omega\\
                y &= 0 && \text{on } \partial\Omega.
            \end{aligned}
        \end{aligned}
    \right.
  \end{equation}

\end{document}
