Question

Determinati elementele multimii A={x apartine Z | 2+b supra 2x-5 apartine Z} unde 3b+5=b+7.

Answer 1

A={X∈Z|  2+b/2x-5∈Z}

3b+5=b+7
3b-b=-5+7
2b=2
b=1

x∈Z⇔2+b/2x-5∈Z
         2+1/2x-5∈Z
         3/2x-5∈Z⇔3 divizibil cu 2x-5⇔2x-5∈D3⇔2x-5={1, 3, -1, -3}

1)2x -5=1
   2x=6
   x=3
   x∈Z

2)2x-5=3
   2x=8
   x=4
   x∈Z

3)2x-5=-1
   2x=4
   x=2
   x∈Z

4)2x-5=-3
   2x=2
   x=1
   x∈Z

Asadar , x={1,2,3,4}

Answer 2

3b+5=b+7
3b-b=7-5
2b=2
b=1

2+b/2x-5 = 2+1/2x-5 = 3/2x-5
2x-5 € divizorilor lui 3
2x-5 € {-3; -1; 1; 3} /+5
2x € {2; 4; 6; 8} /:2
x € {1; 2; 3; 4}