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

its wrong

Answer 2

To solve the equation \( 3m + 54 - \frac{3m}{4} = -2 \), we first want to combine the terms involving \( m \).

1. Combine the \( m \) terms:
\( 3m - \frac{3m}{4} \)

To combine these, we can express \( 3m \) with a common denominator of 4:
\[
3m = \frac{12m}{4}
\]
So,
\[
3m - \frac{3m}{4} = \frac{12m}{4} - \frac{3m}{4} = \frac{12m - 3m}{4} = \frac{9m}{4}
\]

2. Substitute back into the equation:
\[
\frac{9m}{4} + 54 = -2
\]

3. Subtract 54 from both sides:
\[
\frac{9m}{4} = -2 - 54
\]
\[
\frac{9m}{4} = -56
\]

4. To isolate \( m \), multiply both sides by 4:
\[
9m = -56 \cdot 4
\]
\[
9m = -224
\]

5. Now divide by 9:
\[
m = \frac{-224}{9}
\]

Thus, the value for \( m \) that makes the equation true is:
\[
\boxed{\frac{-224}{9}}
\]

Answer 3

Let's carefully solve the equation step-by-step again. The equation is:

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

### Step 1: Combine like terms involving \( m \)

First, let's express \( 3m \) with a common denominator of 4:

\[
3m = \frac{12m}{4}
\]

Substituting this into the equation gives:

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

Now, combine the \( m \) terms:

\[
\left(\frac{12m - 3m}{4}\right) + 54 = -2
\]

This simplifies to:

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

### Step 2: Isolate the term with \( m \)

Next, we'll subtract 54 from both sides to isolate the term with \( m \):

\[
\frac{9m}{4} = -2 - 54
\]
\[
\frac{9m}{4} = -56
\]

### Step 3: Clear the fraction

Now multiply both sides by 4 to get rid of the fraction:

\[
9m = -56 \cdot 4
\]
\[
9m = -224
\]

### Step 4: Solve for \( m \)

Finally, divide by 9:

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

### Final Answer

So the correct value for \( m \) that makes the equation true is:

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

### Verification

Let's substitute \( m = \frac{-224}{9} \) back into the original equation to check:

1. Calculate \( 3m \):

\[
3m = 3 \cdot \frac{-224}{9} = \frac{-672}{9}
\]

2. Calculate \( -\frac{3m}{4} \):

\[
-\frac{3m}{4} = -\frac{3 \cdot \frac{-224}{9}}{4} = \frac{672}{36} = \frac{56}{3}
\]

3. Now plug it into the left side of the original equation:

\[
\frac{-672}{9} + 54 + \frac{56}{3}
\]

Convert 54 to a fraction with a denominator of 9:

\[
54 = \frac{486}{9}
\]
Convert \( \frac{56}{3} \) to a fraction with a denominator of 9:

\[
\frac{56}{3} = \frac{168}{9}
\]

Putting it all together:

\[
\frac{-672 + 486 + 168}{9} = \frac{-672 + 654}{9} = \frac{-18}{9} = -2
\]

Since both sides match, the solution is verified to be:

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

This confirms that the initial solution \( m = \frac{-224}{9} \) is indeed correct. If you believe there’s an error, please provide more details or context, and I’d be happy to resolve it!