Question

(FGV-SP) A soma dos valores inteiros de x que satisfazem simultaneamente às desigualdades |x - 5 | < 3 e |x - 4 | ≤ 1 é? (passo a passo)
A)25
B)13
C)16
D)18
E)21

Answer 1

$|x-5|\ \textless \ 3=\ \textgreater \ -3\ \textless \ x-5\ \textless \ 3=\ \textgreater<strong></strong> \ 2\ \textless \ x\ \textless \ 8-\ \textgreater \ S1=$ {x∈Z/$2\ \textless \ x\ \textless \ 8$}
$|x-4|\ \textgreater \ =1=\ \textgreater \ x-4\ \textgreater \ = -1$ ou $x-4 \geq -1$
$x-4 \leq -1 =\ \textgreater \ x \leq 3$
$x-4 \geq 1=\ \textgreater \ x \geq 5$
S2 = {x∈Z/ $x \leq e$ ou $x \geq 5$}
S = (S1 inter S2) ={x∈Z/($2\ \textless \ x \leq 3$)∪($5 \leq x\ \textless \ 8$)} = {3,5,6,7}
Soma = 3+5+6+7 = 21
Letra E) 21