Set 2: Linear Inequalities

Choice A is correct. Choice A is the correct answer. Split into two separate compound inequalities. 1. Positive Case: $4< x + 2 < 8 \rightarrow 2 < x < 6$ 2. Negative Case: $4< -(x + 2) < 8 \rightarrow 4 < -x - 2 < 8$ - Add 2: $6< -x < 10$ - Multiply by -1: $-6 > x > -10$ (Reverse!) - Rewrite: $-10 < x < -6$ 3. Combine: $2< x < 6$ or $-10 < x < -6$ Strategic Tip: This describes two intervals symmetric around the center (-2). Choice B is incorrect because it misses the negative interval. Choice C is incorrect because it misses the positive interval. Choice D is incorrect because it represents the "hole" in the middle.