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

Question

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 isolate the terms involving \( m \).

1. Combine the remaining terms:

   ( 3m - \frac{3m}{4} + 54 = -2 )

2. To combine \( 3m \) and \(-\frac{3m}{4}\), convert \( 3m \) to a fraction with a denominator of 4:

   ( 3m = \frac{12m}{4} )

   So we can rewrite:

   ( \frac{12m}{4} - \frac{3m}{4} = \frac{12m - 3m}{4} = \frac{9m}{4} )

3. Substitute this back into the equation:

   ( \frac{9m}{4} + 54 = -2 )

4. Now, move 54 to the right side of the equation:

   ( \frac{9m}{4} = -2 - 54 )

   ( \frac{9m}{4} = -56 )

5. To eliminate the fraction, multiply both sides by 4:

   ( 9m = -224 )

6. Now, divide by 9 to solve for \( m \):

   ( m = \frac{-224}{9} )

Thus, the value of \( m \) that makes the equation true is:

\[ m = \frac{-224}{9} \]