What value will make the equation 3m+54−3m4=−2

Question

true? Write your answer as a fraction.(1 point)

Answer 1

To solve the equation \( 3m + 54 - \frac{3m}{4} = -2 \), we first want to eliminate the fraction.

1. Multiply every term by 4 to eliminate the denominator: \[ 4(3m) + 4(54) - 4\left(\frac{3m}{4}\right) = 4(-2) \] Simplifying, we get: \[ 12m + 216 - 3m = -8 \]

2. Combine like terms: \[ 12m - 3m + 216 = -8 \] This simplifies to: \[ 9m + 216 = -8 \]

3. Subtract 216 from both sides: \[ 9m = -8 - 216 \] Simplifying gives: \[ 9m = -224 \]

4. Finally, divide by 9 to solve for \( m \): \[ m = -\frac{224}{9} \]

Thus, the value of \( m \) that makes the equation true is: \[ \boxed{-\frac{224}{9}} \]