Question

Cum se rezolva 1/3 < 2/x-1 < 8/3 x apartine N

Answer 1

x-1≠0, x≠1
2/(x-1) este pozitiv ⇒x>1
inmultim inecuatia cu 3
1<6/(x-1)<8 inmultim cu x-1 (pozitiv) si avem doua inecuatii
x-1<6, x<7, x∈{2,3,4,5,6}
8(x-1)>6, x-1>3/4, x>1,75, x∈{2,3,4,5,6,7,8......}
intersectam cele 2 multimi
S={2,3,4,5,6}