Question

Determinați numerele întregi x care verifica relațiile:
a) |x|<3
B)|x|>=5
C)|2x+5|<=3
D)|3x+3|>=6

Answer 1

$\it a)\ |x|<3 \Rightarrow -3<x<3 \Rightarrow x\in\{-2,\ -1,\ 0,\ 1,\ 2\}\\ \\ b)\ \ |x|\geq5 \Rightarrow x\leq-5\ \c{s}i\ x\geq5 \Rightarrow x\in \mathbb{Z}\backslash\{-4,\ -3,\ -2,\ -1,\ 0,\ 1,\ 2,\ 3,\ 4\}\\ \\ \\ c)\ |2x+5|\leq3 \Rightarrow -3\leq2x+5\leq3|_{-5} \Rightarrow -8\leq2x\leq-2|_{:2} \Rightarrow \\ \\ \Rightarrow -4\leq x\leq-1 \Rightarrow x\in\{-4,\ -3,\ -2,\ -1 \}$