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=
.

Answer 1

Let's first isolate \(m\) in the equation \(3m + 54 - \frac{3m}{4} = -2\).

1. Combine the \(m\) terms on the left side.

To do that, we can rewrite \(3m\) as \(\frac{12m}{4}\):

\[ \frac{12m}{4} - \frac{3m}{4} + 54 = -2 \]

2. Combine the fractions with common denominators:

\[ \frac{12m - 3m}{4} + 54 = -2 \]

\[ \frac{9m}{4} + 54 = -2 \]

3. Next, isolate \(\frac{9m}{4}\) by subtracting 54 from both sides:

\[ \frac{9m}{4} = -2 - 54 \]

\[ \frac{9m}{4} = -56 \]

4. Now multiply both sides by 4 to eliminate the fraction:

\[ 9m = -56 \cdot 4 \]

\[ 9m = -224 \]

5. Finally, divide by 9 to solve for \(m\):

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

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

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