5
algebra

Solve: x+2>4|x + 2| > 4

A

x>2x > 2 or x<6x < -6

B

6<x<2-6 < x < 2

C

x>2x > 2

D

x<6x < -6

Correct Answer: A

Choice A is the correct answer. "GreatOR" splits into two outward cases.

  1. Case 1: x+2>4x>2x + 2 > 4 \rightarrow x > 2
  2. Case 2: x+2<4x<6x + 2 < -4 \rightarrow x < -6
  3. Combine: x>2x > 2 or x<6x < -6

?�� Strategic Tip: Absolute value represents distance. Distance >4> 4 means further away than 4 units in either direction.

Choice B is incorrect because it represents x+2<4|x+2| < 4 (distance less than 4). Choice C is incorrect because it misses the negative case. Choice D is incorrect because it misses the positive case.