Let $x_1\in(0,1)$ and $a_1,\ldots,a_n\ge-1$ reals. We know that
\begin{equation} \prod_{i=1}^n (1+x_1a_i) < 1 \end{equation}
Does it then also hold true that
\begin{equation} \prod_{i=1}^n (1+x_2a_i) < 1 \end{equation}
where $x_2$ is some other real in $(0,1)$?
This is somewhat clear for $n=1$, but I'm not sure about $n$ in general.