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To solve the equation \( 3m + 54 - \frac{3m}{4} = -2 \), let's first eliminate the fraction by finding a common denominator.
1. Rewrite the equation:
\[ 3m + 54 - \frac{3m}{4} = -2 \]
2. To eliminate the fraction, we can multiply the entire equation by 4:
\[ 4(3m) + 4(54) - 4\left(\frac{3m}{4}\right) = 4(-2) \]
This simplifies to:
\[ 12m + 216 - 3m = -8 \]
3. Combine like terms:
\[ (12m - 3m) + 216 = -8 \]
\[ 9m + 216 = -8 \]
4. Isolate \( m \):
\[ 9m = -8 - 216 \]
\[ 9m = -224 \]
5. Divide both sides by 9:
\[ m = \frac{-224}{9} \]
So the value for \( m \) that makes the equation true is:
\[ m = \frac{-224}{9} \]