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Please, help me to determine the set A={x integer/x=(6n-7)/(2n+1), n integer}. Thank you!

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nena1993 | Student, Grade 11 | (Level 2) Honors

Posted June 2, 2009 at 9:51 PM via web

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Please, help me to determine the set A={x integer/x=(6n-7)/(2n+1), n integer}. Thank you!

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted June 3, 2009 at 4:06 AM (Answer #1)

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In order to find out the elements of the set A, we have to notice that the property of the set is that all it's elements are integer numbers (x integer).

For x to be integer, (2n+1) has to be the divisor of the

(6n-7).

(6n-7)=3(2n+1)-10

If we divide the expression above, with (2n+1), the result will be:

(6n-7)/(2n+1)=3-10/(2n+1)

But x=(6n-7)/(2n+1) and x integer, so, in order to obtain x integer, (2n+1) has to be a divisor of 10.

D10=+/-2;+/-5;+/-1;+/-10

(2n+1)=1, 2n=0, n=0, x=(6*0-7)/(2*0+1)=-7/1=-7

(2n+1)=-1,2n=-2,n=-1, x=(6*(-1)-7)/(2*(-1)+1)=13

(2n+1)=2, 2n=1, n=1/2 not integer

(2n+1)=-2, 2n=-3, n=-3/2 not integer

(2n+1)=5, 2n=4, n=2,x=(6*(2)-7)/(2*(2)+1)=5/5=1

(2n+1)=-5, 2n=-6, n=-3, x=(6*(-3)-7)/(2*(-3)+1)=5

(2n+1)=10, 2n=9, n=9/2 not integer

(2n+1)=-10, 2n=-11, n=-11/2 not integer

A={-7,1,5,13}

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