Q: The reciprocal of an integer plus the reciprocal of two times the integer plus two equals two-thirds Find the integer?

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??? explain better.

A negative integer. Every time.

Then, if the exponent is a positive integer, the value is 1 multiplied by the base repeatedly, exponent times. If the exponent is a negative integer then it is the reciprocal of the above value.In either case, it is NOT the base multiplied by itself an exponent number of times.

Yes. The square of an integer is just the number times itself. For any two whole numbers that are multiplied, the answer is always an integer (i.e. no decimals).

-60

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2

It is 2.

??? explain better.

9

80

This question can be expressed algebraically as: (1/n) + (1/(2n)) + 2 = 23, (1/n) + (1/(2n)) =21, ((1+2)/(2n)) = 21, (3/(2n)) = 21, or 2n = (3/21), 2n = (1/7), so n = (1/14). This, by the way, is an elementary algebraic proof that the solution to the above relation is (1/14). Anyway, to answer the question, reread the question: "[What integer is such that] the reciprocal of the integer...". notice, the reciprocal of (1/14) is 14, which is the integer in question! ^_^

4

Call the unknown integer x. Then, from the problem statement, x - 3/x = 26/3, or:x2 - 3 = 26x/3; or x2 - (26/3)x - 3 = 0x = 9

A negative integer. Every time.

1/2n + 1/(2n+2) = 1/2*[(1/n + 1/(n+1)] = 1/2*(2n+1)/[n*(n+1)] or (2n+1)/[2*n*(n+1)]

4

The equasion would be 10x 1/j = 5x1/9 (if j equals some number) so the answer would be j=18.