Set 12: Linear Inequalities (Advanced)

Choice A is correct. Choice A is the correct answer. Nested absolute value. 1. Outer Layer: $-1 < |x| - 2 < 1$ 2. Add 2: $1< |x| < 3$ 3. Split: This means distance from 0 is between 1 and 3. 4. Intervals: $(1, 3)$ and $(-3, -1)$. 5. Inequality: $1< x < 3$ or $-3 < x < -1$ Strategic Tip: Visualize this on a number line: two symmetric bands away from zero. Choice B is incorrect because it misses the negative band. Choice C is incorrect because it includes the gap $[-1, 1]$. Choice D is incorrect because it includes large numbers.