To solve the equation \(3 - \frac{5}{3}x = 18\), we will isolate \(x\).
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Start by subtracting 3 from both sides:
\[ -\frac{5}{3}x = 18 - 3 \]
Simplifying the right side gives:
\[ -\frac{5}{3}x = 15 \]
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Next, to eliminate the negative sign and the fraction, we can multiply both sides by \(-1\):
\[ \frac{5}{3}x = -15 \]
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Now, multiply both sides by the reciprocal of \(\frac{5}{3}\), which is \(\frac{3}{5}\):
\[ x = -15 \cdot \frac{3}{5} \]
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Calculate the right side:
\[ x = -\frac{45}{5} \]
This simplifies to:
\[ x = -9 \]
Thus, the solution is
\[ \boxed{-9} \]
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