sat-dog

Choice A is correct. It's given that a radio show stated that $3$ times as many people voted in favor of the proposal as people who voted against it. Let $x$ represent the number of people who voted against the proposal. It follows that $3x$ is the number of people who voted in favor of the proposal and $3x-x$, or $2x$, is how many more people voted in favor of the proposal than voted against it. It's also given that a social media post reported that $\mathrm{15,000}$ more people voted in favor of the proposal than voted against it. Thus, $2x=\mathrm{15,000}$. Since $2x=\mathrm{15,000}$, the value of $x$ must be half of $\mathrm{15,000}$, or $\mathrm{7,500}$. Therefore, $\mathrm{7,500}$ people voted against the proposal.

Choice B is incorrect. This is how many more people voted in favor of the proposal than voted against it, not the number of people who voted against the proposal.

Choice C is incorrect. This is the number of people who voted in favor of the proposal, not the number of people who voted against the proposal.

Choice D is incorrect and may result from conceptual or calculation errors.