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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=

3 answers

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, \[ 3m - \frac{3m}{4} = \frac{12m}{4} - \frac{3m}{4} = \frac{12m - 3m}{4} = \frac{9m}{4} \]

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

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

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

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

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

its wrong

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 \( 3m \):

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

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

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

  1. 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!