Question

What value will make the equation $3m+\frac {5}{4}-\frac {3m}{4}=-2$ 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

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

let's first combine the terms involving \(m\). We can rewrite \(3m\) as \(\frac{12m}{4}\), allowing us to express \(3m\) and \(-\frac{3m}{4}\) with a common denominator:

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

Now, substituting this back into the equation gives:

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

Combining the \(m\) terms, we have:

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

This simplifies to:

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

Next, we can combine the fractions on the left:

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

To eliminate the fraction, we can multiply both sides of the equation by \(4\):

\[
9m + 5 = -8.
\]

Next, we isolate \(9m\) by subtracting \(5\) from both sides:

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

Now, we can solve for \(m\) by dividing both sides by \(9\):

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

Thus, the solution is

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