Question: User: 7-n divided by 9-2n equals 1
1. **State the problem:** Solve the equation $$\frac{7-n}{9-2n} = 1$$.
2. **Recall the formula and rules:** To solve an equation with a fraction equal to a number, multiply both sides by the denominator to eliminate the fraction.
3. **Multiply both sides by the denominator:**
$$\frac{7-n}{9-2n} \times (9-2n) = 1 \times (9-2n)$$
which simplifies to
$$7-n = 9-2n$$
4. **Isolate the variable $n$:**
Add $2n$ to both sides:
$$7 - n + 2n = 9 - 2n + 2n$$
which simplifies to
$$7 + n = 9$$
5. **Subtract 7 from both sides:**
$$7 + n - 7 = 9 - 7$$
which simplifies to
$$n = 2$$
6. **Check for restrictions:** The denominator $9-2n$ cannot be zero.
Set denominator equal to zero:
$$9 - 2n = 0$$
$$2n = 9$$
$$n = \frac{9}{2} = 4.5$$
Since $n=2$ is not equal to $4.5$, it is valid.
7. **Final answer:**
$$\boxed{2}$$