The problem is to factor the linear expression $27xy - 18x$. We need to find the correct factored form among the given options.

1. Problem Description

The problem is to factor the linear expression $27xy - 18x$. We need to find the correct factored form among the given options.

2. Solution Steps

To factor the expression $27xy - 18x$, we first find the greatest common factor (GCF) of the terms $27xy$ and $18x$.

The factors of $27$ are $1, 3, 9, 27$.

The factors of $18$ are $1, 2, 3, 6, 9, 18$.

The greatest common factor of $27$ and $18$ is $9$.

Both terms have $x$ as a factor. Therefore, the greatest common factor of $27xy$ and $18x$ is $9x$.

Now, we can factor out $9x$ from the expression:

$27xy - 18x = 9x(3y) - 9x(2) = 9x(3y - 2)$.

Comparing with the given options, we find that $9x(3y - 2)$ is one of the choices.

3. Final Answer

$9x(3y - 2)$