5. Let $[|x|]$ be the integer part of $x$ and $\{x\}=x-[|x|]$, the decimal part of $x$. Solve $2[|x|]=x+2\{x\}$.
(ans. $x=0, \frac{4}{3}, \frac{8}{3}$.
$$
\begin{array}{l}
2[|x|]=x+2\{x\} \Rightarrow 2[|x|]=[|x|]+\{x\}+2\{x\} \Rightarrow[|x|]=3\{x\}<3 \Rightarrow \\
\left.[|x|]=0,1,3 \Rightarrow x=0, \frac{4}{3}, \frac{8}{3} .\right)
\end{array}
$$