A number x is 2 more than the product of its reciprocal and its additive inverse. In what interval does the number lie?

Question

anonymous · Answer

$$x+2=\frac{1}{x}\times (-x)$$

anonymous · Answer

$$x+2=1$$
$$x=-1$$

xishem · Answer

$$x=(-x)(\frac{1}{x})+2$$You have it backwards, I believe, satellite.

msmr · Answer

would the interval be $$-2<x \le0$$?

xishem · Answer

$$x=-1+2=1$$1 is two more than -1*(1/1).

msmr · Answer

oh, if satellite had it backwards that would make sense. The interval would have to be $$0<x \le2$$

msmr · Answer

right?

xishem · Answer

The number lies in an infinite number of different intervals.
$$-1290 \le x \le 2$$$$0.99999 \le x \le 4$$The question isn't specific to what interval it wants. Your answer works, though.

msmr · Answer

it's a multiple choice question so it was the only one that worked. thank you! I'm studying for the AMC 10 and it's not fun. :(