To solve the equation \(3m + \frac{5}{4} - \frac{3m}{4} = -2\), we can start by simplifying and isolating the variable \(m\).
First, let's rewrite the equation clearly:
\[ 3m + \frac{5}{4} - \frac{3m}{4} = -2 \]
Next, we can express \(3m\) with a common denominator of 4:
\[ 3m = \frac{12m}{4} \]
So the equation becomes:
\[ \frac{12m}{4} - \frac{3m}{4} + \frac{5}{4} = -2 \]
Combining the fractions on the left gives:
\[ \frac{12m - 3m + 5}{4} = -2 \] \[ \frac{9m + 5}{4} = -2 \]
Now, multiply both sides by 4 to eliminate the fraction:
\[ 9m + 5 = -8 \]
Next, subtract 5 from both sides:
\[ 9m = -8 - 5 \] \[ 9m = -13 \]
Now, divide both sides by 9:
\[ m = \frac{-13}{9} \]
The value for \(m\) that makes the equation true is:
\[ \boxed{\frac{-13}{9}} \]