numărul natural n verifica relatia​

Răspuns:

Explicație pas cu pas:

Numărul natural n verifica relatia​ 1/2<(n+2)/18<7/9 daca si numai daca:

(n+2)/18<7/9  ⇒9·(n+2)<7·18  Impartim prin 9  ⇒(n+2)<7·2  ⇒n<14-2  ⇒n<12  

 1/2<(n+2)/18  ⇒18<2·(n+2) Impartim prin 2  ⇒9<n+2  ⇒9-2<n  ⇒7<n  ⇒n>7  

⇒Pentru a verifica relatia, n trebuie sa fie >7 si <12  ⇒Varianta corecta de raspuns: c) n∈{8,9,10,11}      

Răspuns:

c)

Explicație pas cu pas:

[tex]\frac{1}{2} < \frac{n+2}{18} < \frac{7}{9} \\\bold{aducem\ la\ acelasi\ numitor:}\\\\\frac{1*9}{2*9} < \frac{n+2}{18} < \frac{7*2}{9*2}\\\\\frac{1*9}{2*9} < \frac{n+2}{18} < \frac{7*2}{9*2}\\\\\frac{9}{18} < \frac{n+2}{18} < \frac{14}{18}\ \bold{|*18} (ca\ sa\ scapam\ de\ numitor)\\\\9 < n+2 < 14\\9-2 < n < 14-2\\7 < n < 12 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\\\.\ \ \ \ \\ \\\ n - numar\ natural | = >[/tex]

=> n∈{8, 9, 10, 11}