Question

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 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:

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