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

Question

true? Write your answer as a fraction.(1 point)
The value for m that makes the equation true is m=
.
Remaining Attempts : 3

Answer 1

To solve the equation \( 3m + 54 - \frac{3m}{4} = -2 \), we can follow these steps:

1. First, we can eliminate the fraction by finding a common denominator. The common denominator for 1 and 4 is 4. We can multiply every term by 4 to eliminate the fraction:

\[ 4(3m) + 4(54) - 4\left(\frac{3m}{4}\right) = 4(-2) \]

This gives us:

\[ 12m + 216 - 3m = -8 \]

2. Now, combine like terms:

\[ 12m - 3m + 216 = -8 \]

This simplifies to:

\[ 9m + 216 = -8 \]

3. Next, we isolate \( m \) by subtracting 216 from both sides:

\[ 9m = -8 - 216 \]

This simplifies to:

\[ 9m = -224 \]

4. Finally, divide both sides by 9 to solve for \( m \):

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

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

\[ \boxed{\frac{-224}{9}} \]