3. If $[x]$ represents the greatest integer not greater than $x$, $\{x\}=x-[x]$, then the solution to the equation $x+2\{x\}=3[x]$ is $\qquad$ .
3. $\frac{5}{3}$.

Substitute $x=[x]+\{x\}$ into the original equation to get $3\{x\}=2[x]$. From $0<\{x\}=\frac{2}{3}[x]<1$, we have $[x]=1,\{x\}=\frac{2}{3}$, thus $x=\frac{5}{3}$.