We are asked to solve for $x$ in the equation $\frac{1}{2}x + \frac{1}{5} = 2$.

1. Problem Description

We are asked to solve for $x$ in the equation $\frac{1}{2}x + \frac{1}{5} = 2$.

2. Solution Steps

First, subtract $\frac{1}{5}$ from both sides of the equation:

$\frac{1}{2}x + \frac{1}{5} - \frac{1}{5} = 2 - \frac{1}{5}$

$\frac{1}{2}x = 2 - \frac{1}{5}$

To subtract the fractions, we need a common denominator. The common denominator for 1 and 5 is

5. $\frac{1}{2}x = \frac{2 \cdot 5}{5} - \frac{1}{5}$

$\frac{1}{2}x = \frac{10}{5} - \frac{1}{5}$

$\frac{1}{2}x = \frac{10-1}{5}$

$\frac{1}{2}x = \frac{9}{5}$

Now, multiply both sides of the equation by 2 to isolate $x$:

$2 \cdot \frac{1}{2}x = 2 \cdot \frac{9}{5}$

$x = \frac{2 \cdot 9}{5}$

$x = \frac{18}{5}$

3. Final Answer

$\frac{18}{5}$