What value will make the equation 3m + 5/4 - (3m)/4 = - 2 true? Write your answer as a fraction . ( 1 point ) The value for m that makes the equation true is m Check answer Remaining Attempts: 2 View previous attempt

1 answer

To solve the equation \(3m + \frac{5}{4} - \frac{3m}{4} = -2\), we can start by simplifying and isolating the variable \(m\).

First, let's rewrite the equation clearly:

\[ 3m + \frac{5}{4} - \frac{3m}{4} = -2 \]

Next, we can express \(3m\) with a common denominator of 4:

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

So the equation becomes:

\[ \frac{12m}{4} - \frac{3m}{4} + \frac{5}{4} = -2 \]

Combining the fractions on the left gives:

\[ \frac{12m - 3m + 5}{4} = -2 \] \[ \frac{9m + 5}{4} = -2 \]

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

\[ 9m + 5 = -8 \]

Next, subtract 5 from both sides:

\[ 9m = -8 - 5 \] \[ 9m = -13 \]

Now, divide both sides by 9:

\[ m = \frac{-13}{9} \]

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

\[ \boxed{\frac{-13}{9}} \]