Given that $x$ is an integer where $1 \le x \le 4$, find the minimum value of $\frac{x}{2} + \frac{2}{x}$.

1. Evaluate the expression for all possible integer values of $x$ and identify the minimum.

For $x=1$: $\dfrac{x}{2}+\dfrac{2}{x}=\dfrac12+2=2.5$

For $x=2$: $\dfrac{x}{2}+\dfrac{2}{x}=1+1=2$

For $x=3$: $\dfrac{x}{2}+\dfrac{2}{x}=\dfrac32+\dfrac23=\dfrac{13}{6}$

For $x=4$: $\dfrac{x}{2}+\dfrac{2}{x}=2+\dfrac12=2.5$

The smallest value is $2$.