To solve 1/x 0, then 1 x > 1/2. Case 2: If x 2x => 1/2 > x. Since we assumed x < 0, all x < 0 satisfy this. Thus, the solution is x 1/2. Option 2 misses the negative values. Option 3 is where 1/x > 2. Option 4 is incorrect because it includes values like 0.1 where 1/0.1=10, which is not < 2.