Answer
$\frac{3}{2}$
Work Step by Step
For A, B, C to be collinear, the slopes of $\overline{AB}$ and $\overline{BC}$ must be equal.
Slope of $\overline{AB}$: $\frac{3-5}{2-x}=\frac{-2}{2-x}$
Slope of $\overline{BC}$: $\frac{-5-3}{4-2}=\frac{-8}{2}=-4$
$\frac{-2}{2-x}=-4$
$-2=-4(2-x)$
$-2=-8+4x$
$6=4x$
$x=\frac{3}{2}$
