Solve: $$ \frac{2 n-7}{-7}=\frac{n-1}{2} $$. Enter a fraction if needed. Provide your answer below: $$ n=\square $$

Question

UpStudy AI · Accepted Answer

We start with the equation
$$
\frac{2n-7}{-7}=\frac{n-1}{2}.
$$
To eliminate the fractions, cross-multiply:
$$
2(2n-7) = -7(n-1).
$$

Expand both sides:
$$
4n - 14 = -7n + 7.
$$

Next, add $$7n$$ to both sides to collect the $$n$$-terms on one side:
$$
4n + 7n - 14 = 7,
$$
which simplifies to
$$
11n - 14 = 7.
$$

Now add 14 to both sides:
$$
11n = 7 + 14,
$$
so
$$
11n = 21.
$$

Finally, divide both sides by 11:
$$
n = \frac{21}{11}.
$$

Thus, the final answer is:
$$
n=\frac{21}{11}.
$$
$$ n = \frac{21}{11} $$

Solve: \( \frac{2 n-7}{-7}=\frac{n-1}{2} \). Enter a fraction if needed. Provide your answer below: \( n=\square \)