Question

Найдите множество натуральных решений неравенства:
a)x/17 < 8/51
б)х/65 < 1/13
в)х/5 < 3/15
г)1/16 < х/8
д)5/12 > х/24

Answer 1

$\displaystyle a)&\,\,\frac{x}{17}\ \textless \ \frac{8}{51}\\\\x\ \textless \ \frac{17*8}{51}\\\\x\ \textless \ \frac{8}3\\\\x= \{1,\,2\}$

$\displaystyle b)&\,\,\frac{x}{65}\ \textless \ \frac{1}{13}\\\\x\ \textless \ \frac{65}{13}\\\\x\ \textless \ 5\\\\x= \{1,\,2,\,3,\,4\}$

$\displaystyle B)&\,\,\frac{x}{5}\ \textless \ \frac{3}{15}\\\\x\ \textless \ \frac{3*5}{15}\\\\x\ \textless \ 1\\\\x= \{\varnothing\}$

$\displaystyle g)\,\,\frac{1}{16}\ \textless \ \frac{x}{8}\\\\x\ \textgreater \ \frac{8}{16}\\\\x\ \textgreater \ \frac{1}2\\\\x\in N$

$\displaystyle d)\,\,\frac{5}{12}\ \textgreater \ \frac{x}{24}\\\\x\ \textless \ \frac{5*24}{12}\\\\x\ \textless \ 5*2\\\\x\ \textless \ 10\\\\x=\{1,\,2,\,3,\,4,\,5,\,6,\,7,\,8,\,9\}$