To solve the equation \( \frac{3m + 5}{4} - \frac{3m}{4} = -2 \), we can begin by simplifying the left-hand side.
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Combine the fractions on the left side: \[ \frac{3m + 5 - 3m}{4} = \frac{5}{4} \]
So the equation becomes: \[ \frac{5}{4} = -2 \]
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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:
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Rewrite the original equation: \[ \frac{3m + 5}{4} - \frac{3m}{4} = -2 \]
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Combine the fractions: \[ \frac{(3m + 5 - 3m)}{4} = -2 \] This simplifies to: \[ \frac{5}{4} = -2 \]
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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.