Respuesta :

ItzMeÆXO

Answer:

x = {3,4,7,12}

n = {12,7,4,3}

(upside down)

Step-by-step explanation:

N = {1,2,3,4,5....}

[tex]\:[/tex]

if n = 1

[tex]\sf{x = \frac{2n+6}{n-2}}[/tex]

[tex]\sf{x = \frac{2(1) + 6}{1 - 2}}[/tex]

[tex]\sf{x = \frac{2 + 6}{-1}}[/tex]

[tex]\sf{x = \frac{8}{-1}}[/tex]

[tex]\sf{x = - 8}[/tex]

  • x not N

[tex]\:[/tex]

if n = 2

[tex]\sf{x = \frac{2n+6}{n-2}}[/tex]

[tex]\sf{x = \frac{2(2) +6}{2-2}}[/tex]

[tex]\sf{x = \frac{4 + 6}{2 - 2}}[/tex]

[tex]\sf{x = \frac{8}{0}}[/tex]

[tex]\sf{x = \infty }[/tex]

  • x not N

[tex]\:[/tex]

if n = 3

[tex]\sf{x = \frac{2n+6}{n-2}}[/tex]

[tex]\sf{x = \frac{2(3) +6}{3-2}}[/tex]

[tex]\sf{x = \frac{6 + 6}{1}}[/tex]

[tex]\sf{x = \frac{12}{1}}[/tex]

[tex]\sf{x = 12}[/tex]

  • x is N

[tex]\:[/tex]

if n = 4

[tex]\sf{x = \frac{2n+6}{n-2}}[/tex]

[tex]\sf{x = \frac{2(4) +6}{4-2}}[/tex]

[tex]\sf{x = \frac{8 + 6}{2}}[/tex]

[tex]\sf{x = \frac{14}{2}}[/tex]

[tex]\sf{x = 7}[/tex]

  • x is N

[tex]\:[/tex]

if n = 5

[tex]\sf{x = \frac{2n+6}{n-2}}[/tex]

[tex]\sf{x = \frac{2(5) +6}{5-2}}[/tex]

[tex]\sf{x = \frac{10 + 6}{3}}[/tex]

[tex]\sf{x = \frac{16}{3}}[/tex]

  • x not N

[tex]\:[/tex]

if n = 6

[tex]\sf{x = \frac{2n+6}{n-2}}[/tex]

[tex]\sf{x = \frac{2(6) +6}{6-2}}[/tex]

[tex]\sf{x = \frac{12 + 6}{4}}[/tex]

[tex]\sf{x = \frac{18}{4}}[/tex]

  • x not N

[tex]\:[/tex]

if n = 7

[tex]\sf{x = \frac{2n+6}{n-2}}[/tex]

[tex]\sf{x = \frac{2(7) +6}{7-2}}[/tex]

[tex]\sf{x = \frac{14 + 6}{5}}[/tex]

[tex]\sf{x = \frac{20}{5}}[/tex]

[tex]\sf{x = 4}[/tex]

  • x is N

[tex]\:[/tex]

if n = 12

[tex]\sf{x = \frac{2n+6}{n-2}}[/tex]

[tex]\sf{x = \frac{2(12) +6}{12-2}}[/tex]

[tex]\sf{x = \frac{24 + 6}{10}}[/tex]

[tex]\sf{x = \frac{30}{10}}[/tex]

[tex]\sf{x = 3}[/tex]

  • x is N

[tex]\:[/tex]

conclusion

  • I found the pattern of numbers that the value of n is 3, 4, 7,12
  • For x, I found the pattern of numbers that the value of x is 12, 7, 4,3

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