In Velleman's "Calculus: a Rigorous Course," Example 9 from Section 1.3 tasks us with computing $ h(h(x)) $, where $ h(x) = \lfloor 5x - 2 \rfloor $.
My initial solution:
\begin{align*} h(\lfloor 5x - 2 \rfloor) &= \lfloor 5(\lfloor 5x \rfloor - 2) - 2 \rfloor \\ &= \lfloor 5\lfloor 5x \rfloor - 10 \rfloor - 2 \\ &= \lfloor 5\lfloor 5x \rfloor \rfloor - 12 \end{align*}
However, the provided solution from the book is:
$ 5\lfloor 5x \rfloor - 12 $
How can I get the correct solution ?