Answer by Daniel for alignment of text between 2 lines in align*

I would say as a good solution the use of the array environment within the align environment:

\begin{align}\begin{array}{l}f(1) = -11\\f(-2)\end{array}\qquad \text{while $q$ satisfies}\qquad\begin{array}{r}q(1) = 11,\\q(-1) = 20  \end{array}\end{align}