Question 89
For a real number $x$, we denote by $\lfloor x\rfloor$ the largest integer less than or equal to $x$ (for example, $\lfloor 2.7\rfloor=2$, $\lfloor\pi\rfloor=3$ and $\lfloor-1.5\rfloor=-2$). We also write $\{x\}=x-\lfloor x\rfloor$.
Find all real numbers $x$ such that
$$
\lfloor x\rfloor\{x\}\lt x-1
$$
Find all real numbers $x$ such that
$$
\lfloor x\rfloor\{x\}\lt x-1
$$