To find the coefficient of \(x\) in the expansion of \(\left( 3x - \frac{2}{x} \right)^5\), we use the binomial theorem:

\(\left( a + b \right)^n = \sum_{k=0}^{n} \binom{n}{k} a^{n-k} b^k\)

Here, \(a = 3x\) and \(b = -\frac{2}{x}\), and \(n = 5\).

We need the term where the power of \(x\) is 1. In the general term:

\(T_k = \binom{5}{k} (3x)^{5-k} \left(-\frac{2}{x}\right)^k\)

The power of \(x\) in \(T_k\) is given by:

\((5-k) - k = 5 - 2k\)

We set \(5 - 2k = 1\) to find \(k\):

\(5 - 2k = 1\)

\(2k = 4\)

\(k = 2\)

Substitute \(k = 2\) into the general term:

\(T_2 = \binom{5}{2} (3x)^{3} \left(-\frac{2}{x}\right)^2\)

\(= \binom{5}{2} \cdot 3^3 \cdot x^3 \cdot \frac{4}{x^2}\)

\(= 10 \cdot 27 \cdot 4 \cdot x\)

\(= 1080x\)

Thus, the coefficient of \(x\) is 1080.