Question

Elementele mulțimii A={x apartine R/|2x|<2}

Answer 1

$A = \Big\{x\in \mathbb_{R}\Big| |2x| < 2\Big\} \\ \\ |2x| <2 \Rightarrow |2|\cdot |x| < 2 \Rightarrow 2\cdot |x| < 2 \Rightarrow |x| < \dfrac{2}{2} \Rightarrow |x| <1 \Rightarrow \\ \\ \Rightarrow -1<x<1 \Rightarrow x\in(-1,1) \Rightarrow \boxed{A = (-1,1)}$