To solve the equation \(\frac{1}{3} + \frac{2}{3} : x = 1\), let's break it down step by step.

First, simplify the left side of the equation:

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

The division symbol ":" can be interpreted as division. So, we rewrite the equation as:

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

Next, simplify the fraction:

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

To combine the fractions, find a common denominator. The common denominator for \(\frac{1}{3}\) and \(\frac{2}{3x}\) is \(3x\):

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

Combine the fractions:

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

To clear the fraction, multiply both sides by \(3x\):

\[
x + 2 = 3x
\]

Subtract \(x\) from both sides:

\[
2 = 2x
\]

Divide both sides by 2:

\[
x = 1
\]

So, the solution to the equation is:

\[
x = 1
\]