it was interesting.

Divide both sides by -x gives you |x| (< or =) 4/-x noting that you will be flipping the direction of the greater than sign since you are dividing by a negative. While you can then go and solve as you would any absolute value, having isolated the absolute value onto one side at this point, you can also see that the only way for the absolute value to be equal to a positive number (absolute values cannot be negative) is if the x value itself is negative. Since any negative number (x > 0) is going to be less than 2, we know that the answer will be B.

Need a better explanation.

A more human-like approach:

1. You first try to solve it conventionally, but quickly find out that it's not the right method.
−x(x)≥4 and −x(-x)≥4 lead to no good answer.

2. You then analyze it logically like how chetan2u explained.
-x|x| must be positive; the element |x| is always positive; so the element -x must become positive. Thus, x must be negative so the answer is B.

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