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Problem Statement:

The problem asks us to find the value of \( x \) given the equation:

\[
\frac{1}{x} + \frac{1}{2x} = 3
\]

Step-by-Step Solution:

1. Combine the Fractions:
The left-hand side of the equation involves two fractions with different denominators, \( x \) and \( 2x \). To combine them, we need a common denominator. The least common denominator (LCD) of \( x \) and \( 2x \) is \( 2x \).

Rewrite each fraction with the common denominator \( 2x \):
\[
\frac{1}{x} = \frac{2}{2x} \quad \text{and} \quad \frac{1}{2x} = \frac{1}{2x}
\]

Now, add the fractions:
\[
\frac{1}{x} + \frac{1}{2x} = \frac{2}{2x} + \frac{1}{2x} = \frac{2 + 1}{2x} = \frac{3}{2x}
\]

So, the equation becomes:
\[
\frac{3}{2x} = 3
\]

2. Eliminate the Fraction:
To eliminate the fraction, multiply both sides of the equation by \( 2x \):
\[
2x \cdot \frac{3}{2x} = 2x \cdot 3
\]

Simplify both sides:
\[
3 = 6x
\]

3. Solve for \( x \):
Divide both sides of the equation by 6 to isolate \( x \):
\[
x = \frac{3}{6} = \frac{1}{2}
\]

Final Answer:

\[
\boxed{\frac{1}{2}}
\]

Verification:

To verify the solution, substitute \( x = \frac{1}{2} \) back into the original equation:
\[
\frac{1}{x} + \frac{1}{2x} = \frac{1}{\frac{1}{2}} + \frac{1}{2 \cdot \frac{1}{2}} = 2 + 1 = 3
\]

The left-hand side equals the right-hand side, confirming that the solution is correct.

Thus, the value of \( x \) is \(\boxed{\frac{1}{2}}\).