What value will make the equation 3m+54−3m4=−2 true? Write your answer as a fraction.(1 point) The value for m that makes the equation true is m= .

Answer 1

To solve the equation \( 3m + 54 - \frac{3m}{4} = -2 \), let's first eliminate the fraction by finding a common denominator.

1. Rewrite the equation: \[ 3m + 54 - \frac{3m}{4} = -2 \]

2. To eliminate the fraction, we can multiply the entire equation by 4: \[ 4(3m) + 4(54) - 4\left(\frac{3m}{4}\right) = 4(-2) \]

This simplifies to: \[ 12m + 216 - 3m = -8 \]

3. Combine like terms: \[ (12m - 3m) + 216 = -8 \] \[ 9m + 216 = -8 \]

4. Isolate \( m \): \[ 9m = -8 - 216 \] \[ 9m = -224 \]

5. Divide both sides by 9: \[ m = \frac{-224}{9} \]

So the value for \( m \) that makes the equation true is: \[ m = \frac{-224}{9} \]