The problem asks us to evaluate the expression $\frac{4}{x} + x$ when $x = \frac{1}{2}$.

1. Problem Description

The problem asks us to evaluate the expression $\frac{4}{x} + x$ when $x = \frac{1}{2}$.

2. Solution Steps

We are given the expression $\frac{4}{x} + x$. We are also given that $x = \frac{1}{2}$.

We substitute the value of $x$ into the expression:

$$\frac{4}{x} + x = \frac{4}{\frac{1}{2}} + \frac{1}{2}$$

To divide by a fraction, we multiply by the reciprocal of the fraction:

$$\frac{4}{\frac{1}{2}} = 4 \times \frac{2}{1} = 4 \times 2 = 8$$

So we have:

$$\frac{4}{\frac{1}{2}} + \frac{1}{2} = 8 + \frac{1}{2}$$

We can write 8 as a fraction with a denominator of 2:

$$8 = \frac{8 \times 2}{2} = \frac{16}{2}$$

Then we have:

$$\frac{16}{2} + \frac{1}{2} = \frac{16 + 1}{2} = \frac{17}{2}$$

We can also write this as a mixed number:

$$\frac{17}{2} = 8\frac{1}{2}$$

3. Final Answer

$\frac{17}{2}$ or $8\frac{1}{2}$