To solve the equation \( \frac{3m + 5}{4} - \frac{3m}{4} = -2 \), we can first combine the terms on the left side.
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Rewrite the left side: \[ \frac{3m + 5 - 3m}{4} = -2 \] This simplifies to: \[ \frac{5}{4} = -2 \]
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Since this equation seems incorrect (as \(\frac{5}{4}\) cannot equal \(-2\)), let's multiply both sides by \(4\) to eliminate the denominator: \[ 5 = -2 \times 4 \] \[ 5 = -8 \]
This also shows a contradiction. It indicates that there might be no value for \(m\) that satisfies the original equation as simplified.
Let's consider the simplification more clearly: The left side can be expressed neatly as: \[ \frac{5}{4} - \frac{3m}{4} = -2 \]
By eliminating the fractions, we know: \[ 5 - 3m = -8 \] Now isolate \(m\):
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Solve for \(3m\): \[ 5 + 8 = 3m \] \[ 13 = 3m \]
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Finally, divide by \(3\): \[ m = \frac{13}{3} \]
Thus, the value for \(m\) that makes the equation true is: \[ m = \frac{13}{3} \]