Choice A is the correct answer. Unwrap the nested absolute value.

1. Outer: $-2 \leq |2x - 1| - 3 \leq 2$
2. Add 3: $1 \leq |2x - 1| \leq 5$
3. Split: Distance is between 1 and 5.
   • Case A: $1 \leq 2x - 1 \leq 5$
     • Add 1: $2 \leq 2x \leq 6 \rightarrow 1 \leq x \leq 3$
   • Case B: $-5 \leq 2x - 1 \leq -1$
     • Add 1: $-4 \leq 2x \leq 0 \rightarrow -2 \leq x \leq 0$
4. Combine: $[-2, 0] \cup [1, 3]$

?�� Strategic Tip:$|u| \in [a, b]$ means $u \in [a, b]$ or $u \in [-b, -a]$.

Choice B is incorrect because it includes the gap $(0, 1)$. Choice C is incorrect because it misses the negative interval. Choice D is incorrect because it includes large numbers.