To solve the equation \( 3m + \frac{5}{4} - \frac{3m}{4} = -2 \), we first need to combine like terms. Let's start by rewriting the equation:
\[ 3m - \frac{3m}{4} + \frac{5}{4} = -2 \]
Next, we can combine the terms with \( m \). We can express \( 3m \) as \( \frac{12m}{4} \) to have a common denominator:
\[ \frac{12m}{4} - \frac{3m}{4} = \frac{12m - 3m}{4} = \frac{9m}{4} \]
So, we can rewrite the equation:
\[ \frac{9m}{4} + \frac{5}{4} = -2 \]
To eliminate the fractions, let's multiply the entire equation by 4:
\[ 9m + 5 = -8 \]
Next, we will isolate \( 9m \) by subtracting 5 from both sides:
\[ 9m = -8 - 5 \]
This simplifies to:
\[ 9m = -13 \]
Now, divide both sides by 9:
\[ m = -\frac{13}{9} \]
Thus, the solution to the equation is:
\[ m = -\frac{13}{9} \]