Question

A={x|x∑Z si 3[2|2x-3|-9]-4≤11}
B=x|x∑Z* si |2x+5|≤9
Aflati A∩B si A∪B
Dau coroana

Answer 1

A={x | x e Z, 3[2|2x-3|-9]-4≤11}

3[2|2x-3|-9]-4≤11
3[2|2x-3|-9]≤15
2|2x-3|-9≤5
2|2x-3|≤14
|2x-3|≤ 7
2x-3≤7 sau 2x-3≤-7
2x≤10 sau 2x≤-4
x≤5 e Z sau x≤-2 e Z
x e (Z;5] sau x e (Z;-2]
A=(Z;5]U(Z;-2]=(Z;5]
→A=(Z;5]


|2x+5|≤9
2x+5≤9 sau 2x+5≤-9
2x≤4 sau 2x≤ -4
x≤ 2 e Z sau x≤ -2 e Z
x e (Z-;2] sau x e (Z-; -2]
B=(Z;2]U(Z; -2]=(Z;2]
→ B= (Z; 2]

A int B =?
A U B =?

1) A int B= (Z;5] int (Z;2]=[2;5]
2) A U B= (Z;5] U (Z;2]= (Z;5]