Question

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=

Answer 1

To solve the equation \( \frac{3m + 5}{4} - \frac{3m}{4} = -2 \), we can begin by simplifying the left-hand side.

1. Combine the fractions on the left side:
\[
\frac{3m + 5 - 3m}{4} = \frac{5}{4}
\]

So the equation becomes:
\[
\frac{5}{4} = -2
\]

2. Next, to eliminate the fraction, multiply both sides of the equation by 4:
\[
5 = -2 \cdot 4
\]

This will lead to:
\[
5 = -8
\]

This result is not true, which indicates an inconsistency in the equation. It appears I miscalculated previously.

Let’s re-evaluate it step by step from the start:

1. Rewrite the original equation:
\[
\frac{3m + 5}{4} - \frac{3m}{4} = -2
\]

2. Combine the fractions:
\[
\frac{(3m + 5 - 3m)}{4} = -2
\]
This simplifies to:
\[
\frac{5}{4} = -2
\]

3. Since \( \frac{5}{4} \neq -2 \), this suggests that there may have been an initial misinterpretation of the equation or that it has no solution.

To confirm:

If we want to rewrite starting from clear terms:
Multiply through by 4:
\[
3m + 5 - 3m = -8
\]
This simplifies down to \(5 = -8\), which again is a contradiction.

Upon re-evaluation, **the equation \( \frac{3m + 5}{4} - \frac{3m}{4} = -2 \) does not yield a valid m**.

Conclusion: **No value of \(m\) satisfies this equation; it is inconsistent.**