problem: What is the smallest value of $x$ such that $|5x - 1| = |3x + 2|$? Express your answer as a common fraction.
solution: There are two cases, when $5x-1=3x+2$ and when $5x-1=-(3x+2).$ The two equations yield $x=\frac{3}{2}$ and $x=-\frac{1}{8},$ respectively, of which $x=\boxed{-\frac{1}{8}}$ is the smaller solution.