Question

Escreva cada conjunto usando a notação de intervalo e represente-o
na reta numérica.

A = {x ∈ R ; −x + 3 >4}
B = {x ∈ R ; −5≤ x − 2 < 4}
C = {x ∈ R ; | x − 3|≤2}
D =A∩B

Answer 1

$A:~-x+3>4\\\\A:~-x>4-3\\\\\boxed{A:~x<-1}\\\\\\B:~-5\le x-2<4\\\\B:~-5+2 \le x<4+2\\\\\boxed{B:~-3 \le x<6}\\\\\\C:~x-3 \le 2~~ou~~x-3 \geq  -2\\\\C:~x \le 2+3~~ou~~x \geq -2+3\\\\\boxed{C:~x \le 5~~ou~~ x \geq 1}$

Achamos o conjunto D mais simplesmente pelo método gráfico (retas numéricas).

D: -3 ≤ x < -1