Let’s carefully go through the equation step by step to find the correct value of \( m \) that satisfies the equation \( 3m + 54 - \frac{3m}{4} = -2 \).
Step 1: Rewrite the equation
Starting from:
\[
3m + 54 - \frac{3m}{4} = -2
\]
Step 2: Eliminate the fraction
To eliminate the fraction, we can multiply the entire equation by 4 to avoid dealing with the fraction:
\[
4(3m) + 4(54) - 4\left(\frac{3m}{4}\right) = 4(-2)
\]
This gives us:
\[
12m + 216 - 3m = -8
\]
Step 3: Combine like terms
Now, combine \( 12m \) and \( -3m \):
\[
(12m - 3m) + 216 = -8
\]
This simplifies to:
\[
9m + 216 = -8
\]
Step 4: Isolate \( m \)
Next, subtract 216 from both sides:
\[
9m = -8 - 216
\]
Simplifying gives:
\[
9m = -224
\]
Step 5: Solve for \( m \)
Now, divide both sides by 9:
\[
m = \frac{-224}{9}
\]
Since this value seems to match my previous calculation, let's ensure everything is accurate and check the initial setup again.
Step 6: Check the substitution
Let’s substitute \( m = \frac{-224}{9} \) back into the original equation to verify:
-
Calculate \( 3m \):
\[
3 \times \frac{-224}{9} = \frac{-672}{9}
\]
-
Calculate \( \frac{3m}{4} \):
\[
\frac{\frac{-672}{9}}{4} = \frac{-672}{36} = \frac{-224}{12} = \frac{-56}{3}
\]
-
Now substitute back into the equation:
\[
3m + 54 - \frac{3m}{4} = -2
\]
\[
\frac{-672}{9} + 54 + \frac{56}{3}
\]
-
Convert \( 54 \) to a fraction with a common denominator:
\[
54 = \frac{486}{9}
\]
Also, convert \( \frac{56}{3} \):
\[
\frac{56}{3} = \frac{168}{9}
\]
-
Combine them:
\[
\frac{-672}{9} + \frac{486}{9} + \frac{168}{9} = \frac{-672 + 486 + 168}{9} = \frac{-672 + 654}{9} = \frac{-18}{9} = -2
\]
As we can see, substituting back confirms that the value \( m = \frac{-224}{9} \) does satisfy the original equation.
Final conclusion
The solution given previously is indeed correct:
\[
\boxed{\frac{-224}{9}}
\]
If there was any misunderstanding or a specific aspect you thought was incorrect, please clarify and I will address it!
