Solve This Expression: What Does 100 : (2x/18a) - ((3x/a) + 14a - 3x) Equal?

To solve this problem, we'll simplify the given expression step by step:

The problem asks us to evaluate the expression:

$100:\frac{2x}{18a}-(\frac{3x}{a}+14a-3x)$

Step 1: Simplify the expression $\frac{2x}{18a}$.

We can simplify $\frac{2x}{18a}$ by reducing the fraction:

$\frac{2x}{18a} = \frac{x}{9a}$

Step 2: Interpret the operation $100:\frac{x}{9a}$.

The operation "100 divided by" implies multiplying by the reciprocal:

$100:\frac{x}{9a} = 100 \times \frac{9a}{x} = \frac{900a}{x}$

Step 3: Simplify the terms within the parentheses.

The expression inside the parentheses is:

$(\frac{3x}{a} + 14a - 3x)$

Step 4: Simplify the entire expression using the expression outside the parentheses.

So, substituting back and simplifying, we have:

$\frac{900a}{x} - \frac{3x}{a} - 14a + 3x$

Therefore, the solution to the problem in simplified form is $900\frac{a}{x} - 3\frac{x}{a} - 14a + 3x$.

Thus, the correct choice from the provided options is:

Choice 4: $900\frac{a}{x} - 3\frac{x}{a} - 14a + 3x$