2
algebra

Solve: ∣∣x∣−2∣<1||x| - 2| < 1

A

−3<x<−1-3 < x < -1 or 1<x<31 < x < 3

B

1<x<31 < x < 3

C

−3<x<3-3 < x < 3

D

x<−1x < -1 or x>1x > 1

Correct Answer: A

Choice A is the correct answer. Nested absolute value.

  1. Outer Layer: −1<∣x∣−2<1-1 < |x| - 2 < 1
  2. Add 2: 1<∣x∣<31 < |x| < 3
  3. Split: This means distance from 0 is between 1 and 3.
  4. Intervals: (1,3)(1, 3) and (−3,−1)(-3, -1).
  5. Inequality: 1<x<31 < x < 3 or −3<x<−1-3 < 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][-1, 1]. Choice D is incorrect because it includes large numbers.

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Linear Functions Set 79