3. Find the number of solutions to the equation $x=\left[\frac{x}{2}\right]+\left[\frac{x}{3}\right]+\left[\frac{x}{5}\right]$ (here, as usual, $[x]$ is the integer part of the number $x$, i.e., the greatest integer not exceeding the number $x$).
1.II.3. Let $x=30 k+d$, where $k \in \mathbb{Z}$, and $d \in\{0,1, \ldots, 29\}$. Substituting this expression into the given equation, we get

$$
30 k+d=15 k+\left[\frac{d}{2}\right]+10 k+\left[\frac{d}{3}\right]+6 k+\left[\frac{d}{5}\right]
$$

or $k=d-\left[\frac{d}{2}\right]-\left[\frac{d}{3}\right]-\left[\frac{d}{5}\right]$. Thus, for each of the thirty values of $d$, there is a unique value of $k$ such that $x=30 k+d$ is a solution to the given equation.

Answer: 30 solutions.