Question

Sa se rezolve inecuatia>
|$\frac{3n+1}{n} -3$|>$\frac{1}{5}$, n∈R

Answer 1

[tex]| \frac{3n+1}{n} -3| \ \textgreater \ \frac{1}{5} \\ \\ |\frac{3n+1}{n}-3|\ \textgreater \ \frac{1}{5} , n \neq 0 \\ \\ I. \frac{3n+1}{n} -3\ \textgreater \ \frac{1}{5}, \frac{3n+1}{n} -3 \geq 0 \\ \\ n-apartine (0;5), n\ \textgreater \ 0 \\ \\ n -apartine(0;5) \\ \\ II. -( \frac{3n+1}{n}-3)\ \textgreater \ \frac{1}{5} , \frac{3n+1}{n}-3\ \textless \ 0 \\ \\ n-apartine (-5;0), n\ \textless \ 0 \\ \\ n-apartine (-5;0) [/tex]
Din I si II ⇒
 ⇒n-apartine (-5;0)reunit(0;5), n≠0 ⇒
⇒ n-apartine (-5;0)reunit(0;5)