To solve the equation \( 3 - \frac{5}{3}x = 18 \), follow these steps:
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Start with the original equation: \[ 3 - \frac{5}{3}x = 18 \]
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Subtract 3 from both sides: \[ -\frac{5}{3}x = 18 - 3 \] \[ -\frac{5}{3}x = 15 \]
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To isolate \( x \), multiply both sides by \(-\frac{3}{5}\) (the reciprocal of \(-\frac{5}{3}\)): \[ x = 15 \cdot -\frac{3}{5} \]
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Simplify the right side: \[ x = -\frac{45}{5} \] \[ x = -9 \]
So, the solution is: \[ \boxed{-9} \]