What value will make the equation 3m+54−3m4=−2

Let's solve the equation step by step:

The given equation is:

\[ 3m + 54 - \frac{3m}{4} = -2. \]

First, we want to eliminate the fraction involving \( m \). To do this, we can find a common denominator for the terms involving \( m \). The common denominator between \( 1 \) (the denominator of \( 3m \)) and \( 4 \) (the denominator of \( \frac{3m}{4} \)) is \( 4 \).

We can rewrite the equation as:

\[ 4(3m) + 4(54) - 3m = 4(-2). \]

This simplifies to:

\[ 12m + 216 - 3m = -8. \]

Now, combine like terms:

\[ (12m - 3m) + 216 = -8, \]

which simplifies to:

\[ 9m + 216 = -8. \]

Next, subtract \( 216 \) from both sides:

\[ 9m = -8 - 216, \]
\[ 9m = -224. \]

Now, divide both sides by \( 9 \) to solve for \( m \):

\[ m = \frac{-224}{9}. \]

Thus, the value for \( m \) that makes the equation true is:

\[ m = \frac{-224}{9}. \]