What is the sum of all solutions to |x - 5| = 3?

Split the absolute value equation into two cases: $x-5=3$ gives $x=8$, and $x-5=-3$ gives $x=2$. The sum of the solutions is $8+2=10$, choice D. The solutions are the two points on the number line that are $3$ units from $5$, so they are symmetric about $5$, and their average is $5$; thus their sum is $2\cdot5=10$. Choice C ($8$) is only one of the solutions. Choice B ($5$) is the center. Choice A ($3$) is the distance, not a solution.