Let $\left\{x\right\}$  and $\left[x\right]$  denotes the fractional and integral part of a real number $x$  respectively and $4\left\{x\right\}=x+\left[x\right]$ , then $x$ =

$4\left\{x\right\}=\left[x\right]+\left\{x\right\}+\left[x\right]$ 

$\Rightarrow \left[x\right]=\frac{3}{2}\left\{x\right\}\Rightarrow 0\le \left[x\right]<3/2 \left(\sin ce0\le \left\{x\right\}<1\right)$

$\Rightarrow \left[x\right]=0or1$

If $\left[x\right]=0,\text{\hspace{0.17em}then }\left\{x\right\}=0,if\left[x\right]=1,then\left\{x\right\}=2/3$

$\therefore x=\left[x\right]+\left\{x\right\}=0$  or $1+2/3=5/3$ .