To solve the equation \( \frac{3m + 5}{4} - \frac{3m}{4} = -2 \), we can begin by simplifying the left-hand side.
1. Combine the fractions on the left side:
\[
\frac{3m + 5 - 3m}{4} = \frac{5}{4}
\]
So the equation becomes:
\[
\frac{5}{4} = -2
\]
2. Next, to eliminate the fraction, multiply both sides of the equation by 4:
\[
5 = -2 \cdot 4
\]
This will lead to:
\[
5 = -8
\]
This result is not true, which indicates an inconsistency in the equation. It appears I miscalculated previously.
Let’s re-evaluate it step by step from the start:
1. Rewrite the original equation:
\[
\frac{3m + 5}{4} - \frac{3m}{4} = -2
\]
2. Combine the fractions:
\[
\frac{(3m + 5 - 3m)}{4} = -2
\]
This simplifies to:
\[
\frac{5}{4} = -2
\]
3. Since \( \frac{5}{4} \neq -2 \), this suggests that there may have been an initial misinterpretation of the equation or that it has no solution.
To confirm:
If we want to rewrite starting from clear terms:
Multiply through by 4:
\[
3m + 5 - 3m = -8
\]
This simplifies down to \(5 = -8\), which again is a contradiction.
Upon re-evaluation, **the equation \( \frac{3m + 5}{4} - \frac{3m}{4} = -2 \) does not yield a valid m**.
Conclusion: **No value of \(m\) satisfies this equation; it is inconsistent.**