Question

1. Numarul natural n pentru care fractia $\frac{n-1}{n-3}$ este echivalenta cu fractia $\frac{18}{14}$ este egal cu:
A) 8
B) 9
C) 10
D) 12
2. Daca n∈N si $\frac{5}{6}\ \textless \ \frac{n+3}{8}\ \textless \ \frac{11}{10}$ atunci n este:
A) 4
B) {4, 5}
C) {4, 6}
D) 5
Va rog!!!! (dau coronita)

Answer 1

$\frac{n-1}{n-3}=\frac{18}{14} \\ \\ 14(n-1)=18(n-3) \\ \\ 14n-14=18n-54 \\ \\ 14n+40=18n \\ \\ 4n=40 \\ \\ n=10$
Raspuns c
$\frac{5}{6}<\frac{n+3}{8}<\frac{11}{10} \\ \\ \frac{100}{120}<\frac{15(n+3)}{120}<\frac{132}{120} \\ \\ 100<15(n+3)<132 \\ \\ 100<15n+45<132 \\ \\ 55<15n<87 \\ \\ \frac{55}{15}<n<\frac{87}{15} \\ \\ \frac{60}{15}\leq n\leq\frac{75}{15} \\ \\ 4\leq n\leq5 \\ \\ n\in\{4,5\}$
Raspuns b