Question

1. \\(\frac{n - 6}{3} = \frac{n - 2}{9}\\)

Explanation:

Step1: Eliminate the denominator

Multiply both sides of the equation $\frac{n - 6}{3}=\frac{n - 2}{9}$ by 9 (the least common multiple of 3 and 9) to get rid of the denominators.
$$9\times\frac{n - 6}{3}=9\times\frac{n - 2}{9}$$
Simplify both sides: $3(n - 6)=n - 2$.

Step2: Expand the left - hand side

Use the distributive property $a(b + c)=ab+ac$ to expand $3(n - 6)$.
$$3n-18=n - 2$$

Step3: Move the terms with n to one side and constants to the other side

Subtract $n$ from both sides: $3n - n-18=n - n - 2$, which simplifies to $2n-18=-2$.
Then add 18 to both sides: $2n-18 + 18=-2 + 18$.

Step4: Solve for n

Simplify the equation: $2n=16$.
Divide both sides by 2: $n=\frac{16}{2}=8$.

Answer:

$n = 8$