To solve for \( x \) in the equation
\[ 3 - \frac{5}{3}x = 18, \]
follow these steps:
- Subtract 3 from both sides:
\[ -\frac{5}{3}x = 18 - 3 \]
\[ -\frac{5}{3}x = 15. \]
- Multiply both sides by \(-1\):
\[ \frac{5}{3}x = -15. \]
- To isolate \( x \), multiply both sides by the reciprocal of \(\frac{5}{3}\), which is \(\frac{3}{5}\):
\[ x = -15 \times \frac{3}{5}. \]
- Calculate the right-hand side:
\[ x = -\frac{45}{5} = -9. \]
Thus, the solution is
\[ \boxed{-9}. \]