To solve the equation \(3m + 54 - \frac{3m}{4} = -2\), we first want to eliminate the fraction. We can do this by multiplying every term in the equation by 4:
\[ 4(3m) + 4(54) - 4\left(\frac{3m}{4}\right) = 4(-2) \]
This simplifies to:
\[ 12m + 216 - 3m = -8 \]
Next, we combine the like terms \(12m - 3m\):
\[ 9m + 216 = -8 \]
Now, we'll isolate \(9m\) by subtracting 216 from both sides:
\[ 9m = -8 - 216 \] \[ 9m = -224 \]
Now, we divide both sides by 9 to solve for \(m\):
\[ m = \frac{-224}{9} \]
Thus, the value for \(m\) that makes the equation true is:
\[ m = \frac{-224}{9} \]
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