$\because \dfrac{y}{x}=\dfrac{3}{4}$，

$\therefore y=\dfrac{3}{4}x$，

$\because 2z=x$，

$\therefore z=\dfrac{1}{2}x$，

$\therefore \dfrac{x+y}{z}=\dfrac{x+\dfrac{3}{4}x}{\dfrac{1}{2}x}=\dfrac{7}{2}$；

故选：$D$.