What is the sum of all real solutions to |5x - 10| = 3x?

Split $|5x - 10| = 3x$ into two cases. Case 1: $5x - 10 = 3x$ gives $2x = 10$ and $x = 5$. Case 2: $5x - 10 = -3x$ gives $8x = 10$, so $x = \frac{5}{4}$. Both solutions give a nonnegative right side, so both are valid. Check $x = \frac{5}{4}$: $|6.25 - 10| = 3.75 = 3(1.25)$. The sum is $5 + \frac{5}{4} = \frac{25}{4}$, choice A. Choice B (5) is just one solution. Choice C ($\frac{15}{4}$) comes from $3 \cdot \frac{5}{4}$. Choice D (10) comes from doubling 5. The question asks for the sum of all real solutions.