The equation kx - 7 = 3x + 2 has exactly one solution for every value of k except one. What is that excluded value of k?

Collect the $x$-terms on one side: $kx - 3x = 2 + 7$, so $(k - 3)x = 9$. When $k \neq 3$, divide by $k - 3$ to get exactly one solution, $x = \frac{9}{k-3}$. When $k = 3$, the equation becomes $0 \cdot x = 9$, which is false for every $x$, so there is no solution. The excluded value is 3, choice C. Choice A (7) and choice B (2) are constants from the original equation that do not affect the coefficient of $x$. Choice D ($-3$) comes from a sign error when moving $3x$, which produces $k + 3$ instead of $k - 3$.