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

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

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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

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Other answers:

would the interval be \[-2
\[x=-1+2=1\]1 is two more than -1*(1/1).
oh, if satellite had it backwards that would make sense. The interval would have to be \[0
right?
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.
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. :(

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