Answer: A. $w = -130xv$

Explanation:1. Understand the given equation: The equation is $v = -\dfrac{w}{130x}$. It relates distinct positive numbers $v, w,$ and $x$. We need to express $w$ in terms of $v$ and $x$.

2. Isolate w: The term containing $w$ is $-\dfrac{w}{130x}$. To isolate $w$, we want to remove the denominator ($130x$) and the negative sign.

Step 1: Multiply both sides by $130x$. Since $x$ is a positive number, $130x$ is also positive (assuming $130$ is a positive constant, which it is). $130x \times v = 130x \times \left(-\dfrac{w}{130x}\right)$ $130xv = -w$

Step 2: Multiply both sides by $-1$ to solve for $w$: $-1 \times (130xv) = -1 \times (-w)$ $-130xv = w$ So, $w = -130xv$.

3. Compare with the given options: [A] $w = -130xv$ - This matches our result. [B] $w = -\dfrac{130v}{x}$ - Incorrect. [C] $w = -\dfrac{x}{130v}$ - Incorrect. [D] $w = v + 130x$ - Incorrect.

4. Conclusion: The equation that correctly expresses w in terms of v and x is $w = -130xv$.