对齐环境中的缩进

Question

如何得到这个方程的对称分离：

我不想在第一个小于或等于号前面有这个间隙。我目前使用对齐环境，但我不确定这是否是最好的方法。

一个简单的例子：

\documentclass[12pt,twoside]{report}

\usepackage[utf8]{inputenc}
\usepackage[a4paper,width=150mm,top=25mm,bottom=25mm]{geometry}

\setlength{\parindent}{0pt}

\usepackage{amsmath, amssymb, amsthm, mathtools}

\DeclarePairedDelimiter\betr{\lvert}{\rvert}
\newcommand{\E}[1]{\mathbb{E}\left[{#1}\right]} %Expectation
\newcommand{\bet}[3]{\beta^{{#1}}_{{#2}}({#3})}

\begin{document}
    \begin{align*}
        &\E{\betr{D_x\bet{n}{k}{\mathcal{P}_n}}^4}& \leq 16\E{\left[\mathcal{P}_n(B_{r_n}(x))\right]^{4(k+1)}}& \leq 16\E{\left[Poi(r_*f^*)\right]^{4(k+1)}}, \\
        &\E{\betr{D_x\bet{n}{k}{\mathcal{X}_n}}^4}& \leq 16\E{\left[\mathcal{X}_n(B_{r_n}(x))\right]^{4(k+1)}}& \leq 16\E{\left[Bin\left(n,\frac{r_*f^*}{n}\right)\right]^{4(k+1)}}.
    \end{align*}
\end{document}

Answer 1

\documentclass[12pt,twoside]{report}

\usepackage[utf8]{inputenc}
\usepackage[a4paper,width=150mm,top=25mm,bottom=25mm]{geometry}

\setlength{\parindent}{0pt}

\usepackage{amsmath, amssymb, amsthm, mathtools}

\DeclarePairedDelimiter\betr{\lvert}{\rvert}
\newcommand{\E}[1]{\mathbb{E}\left[{#1}\right]} %Expectation
\newcommand{\bet}[3]{\beta^{{#1}}_{{#2}}({#3})}

\begin{document}
    \begin{alignat*}{2}
        \E{\betr{D_x\bet{n}{k}{\mathcal{P}_n}}^4}& \leq 16\E{\left[\mathcal{P}_n(B_{r_n}(x))\right]^{4(k+1)}}&&\leq 16\E{\left[Poi(r_*f^*)\right]^{4(k+1)}}, \\
        \E{\betr{D_x\bet{n}{k}{\mathcal{X}_n}}^4}& \leq 16\E{\left[\mathcal{X}_n(B_{r_n}(x))\right]^{4(k+1)}}&& \leq 16\E{\left[Bin\left(n,\frac{r_*f^*}{n}\right)\right]^{4(k+1)}}.
    \end{alignat*}
\end{document}