To solve the equation \( 3m + 54 - \frac{3m}{4} = -2 \), let's first isolate the terms involving \( m \).
1. Combine the remaining terms:
\(
3m - \frac{3m}{4} + 54 = -2
\)
2. To combine \( 3m \) and \(-\frac{3m}{4}\), convert \( 3m \) to a fraction with a denominator of 4:
\(
3m = \frac{12m}{4}
\)
So we can rewrite:
\(
\frac{12m}{4} - \frac{3m}{4} = \frac{12m - 3m}{4} = \frac{9m}{4}
\)
3. Substitute this back into the equation:
\(
\frac{9m}{4} + 54 = -2
\)
4. Now, move 54 to the right side of the equation:
\(
\frac{9m}{4} = -2 - 54
\)
\(
\frac{9m}{4} = -56
\)
5. To eliminate the fraction, multiply both sides by 4:
\(
9m = -224
\)
6. Now, divide by 9 to solve for \( m \):
\(
m = \frac{-224}{9}
\)
Thus, the value of \( m \) that makes the equation true is:
\[
m = \frac{-224}{9}
\]