Question

Aflati x∈ N, astfel incat $\frac{1}{2 } \ \textless \ \frac{3}{x-1} \leq \frac{9}{2}$

Answer 1

conditia de existenta 
x-1≠0,x≠1
se studiaza doua inecuatii
1) 1/2<3/(x-1)
x-1<6
x<7si deoarece x∈N solutia este x={0,1,2,3,4,5,6}
2) 3/(x-1)≤9/2
9x-9≥6
9x≥15
x≥15/9
x≥5/3
x≥2
solutia este data de intersectia celor dou si deci 
S={2,3,4,5,6}