Something

\documentclass[]{article}
\usepackage{amsmath}
\begin{document}
\begin{align*}
X' &>    \frac{m}{(d')^3 r^{k'} (k'+1)} &\\
           &\geq \frac{m}{8 d^3 r^{k'} (k'+1)}& \quad \text{(since $d' \leq 2d$)}\\
           &\geq \frac{m}{8 d^3 r^{k} (k+1)}  & \quad \text{(since $d' > d$, implying $k' \leq k$)}\\
           &\geq \frac{m}{1 \; 2 \; 3 \; 4 \; 5 \; 6 \; 7 \; 8 \; 9 \; 10 \; 1 \; 2 \; 3 \; 4 \; 5 \; 6 \; 7 \; 8 \; 9 \; 10 \; } &\\
\end{align*}

or (align peculiarity):
\begin{align*}
X' &>    \frac{m}{(d')^3 r^{k'} (k'+1)} &&\\
           &\geq \frac{m}{8 d^3 r^{k'} (k'+1)}&& \quad \text{(since $d' \leq 2d$)}\\
           &\geq \frac{m}{8 d^3 r^{k} (k+1)}  && \quad \text{(since $d' > d$, implying $k' \leq k$)}\\
           &\geq \frac{m}{1 \; 2 \; 3 \; 4 \; 5 \; 6 \; 7 \; 8 \; 9 \; 10 \; 1 \; 2 \; 3 \; 4 \; 5 \; 6 \; 7 \; 8 \; 9 \; 10 \; } &&\\
\end{align*}

\end{document}