Given that (1/x) > -3, which of the following cannot . .

Thinking through the problem logically is going to be faster than building equations on this one: we know that 1/x > -3. This means that any positive answers will definitely work (since any positive number is going to be greater than negative three) and any negative whole number answers will definitely work (since a negative fraction is going to be greater than negative three). This gets us down to C and D — we know that 1 over a fraction will equal the reciprocal of the fraction, so we'll end up with -2 > -3 and -3 > -3, of which only the first works. So the correct answer is D.