What is the larger of the two solutions to |4x - 8| = 3x?

Split $|4x - 8| = 3x$ into two cases. Case 1: $4x - 8 = 3x$ gives $x = 8$. Case 2: $4x - 8 = -3x$ gives $7x = 8$, so $x = \frac{8}{7}$. Both solutions give a nonnegative right side $3x$, so both are valid. Check $x = 8$: $|24| = 24$. Check $x = \frac{8}{7}$: $\left|\frac{32}{7} - 8\right| = \frac{24}{7} = 3 \cdot \frac{8}{7}$. The larger solution is 8, choice C. Choice A ($\frac{8}{7}$) is the smaller solution. Choice B (4) and choice D (12) do not satisfy the equation: $|16 - 8| = 8 \neq 12$ and $|48 - 8| = 40 \neq 36$.