To solve the equation \( 3m + 54 - \frac{3m}{4} = -2 \), we will manipulate the equation step by step.
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Combine like terms. First, let's rewrite the equation for clarity: \[ 3m + 54 - \frac{3m}{4} = -2 \]
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To combine \( 3m \) and \( -\frac{3m}{4} \), we'll convert \( 3m \) into a fraction with a denominator of 4: \[ 3m = \frac{12m}{4} \] Thus, we have: \[ \frac{12m}{4} - \frac{3m}{4} = \frac{12m - 3m}{4} = \frac{9m}{4} \]
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Substitute this back into the equation: \[ \frac{9m}{4} + 54 = -2 \]
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Now, isolate \( \frac{9m}{4} \): \[ \frac{9m}{4} = -2 - 54 \] Simplifying the right side: \[ \frac{9m}{4} = -56 \]
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To eliminate the fraction, multiply both sides by 4: \[ 9m = -56 \cdot 4 \] Simplifying further: \[ 9m = -224 \]
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Finally, solve for \( m \) by dividing both sides by 9: \[ m = \frac{-224}{9} \]
Thus, the value for \( m \) that makes the equation true is: \[ m = \frac{-224}{9} \]
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