What value will make the equation 3m+54−3m4=−2%0D%0A3%0D%0A𝑚%0D%0A+%0D%0A5%0D%0A4%0D%0A−%0D%0A3%0D%0A𝑚%0D%0A4%0D%0A=%0D%0A−%0D%0A2%0D%0A true? Write your answer as a fraction.(1 point)%0D%0AThe value for m that makes the equation true is m=%0D%0A𝑚%0D%0A=

To solve the equation \( 3m + 54 - \frac{3m}{4} = -2 \), we will manipulate the equation step by step.

1. Combine like terms. First, let's rewrite the equation for clarity:
\[
3m + 54 - \frac{3m}{4} = -2
\]

2. To combine \( 3m \) and \( -\frac{3m}{4} \), we'll convert \( 3m \) into a fraction with a denominator of 4:
\[
3m = \frac{12m}{4}
\]
Thus, we have:
\[
\frac{12m}{4} - \frac{3m}{4} = \frac{12m - 3m}{4} = \frac{9m}{4}
\]

3. Substitute this back into the equation:
\[
\frac{9m}{4} + 54 = -2
\]

4. Now, isolate \( \frac{9m}{4} \):
\[
\frac{9m}{4} = -2 - 54
\]
Simplifying the right side:
\[
\frac{9m}{4} = -56
\]

5. To eliminate the fraction, multiply both sides by 4:
\[
9m = -56 \cdot 4
\]
Simplifying further:
\[
9m = -224
\]

6. Finally, solve for \( m \) by dividing both sides by 9:
\[
m = \frac{-224}{9}
\]

Thus, the value for \( m \) that makes the equation true is:
\[
m = \frac{-224}{9}
\]