The variable y varies inversely with x. When x=7, y=10. What is the value of y when x=14?

Inverse variation means $xy$ is constant. From $x = 7$ and $y = 10$, the constant is $k = 70$. When $x = 14$, $y = \frac{70}{14} = 5$, choice D. Since $x$ doubled, $y$ must be cut in half: $10 \div 2 = 5$. Choice A (20) doubles $y$, treating the relationship as direct. Choice B (7) is the original $x$-value. Choice C (2.5) halves $y$ twice, which would match $x = 28$. For inverse variation, multiplying $x$ by a factor divides $y$ by the same factor.