Question

|x+1|(|2x+1|-5)<0 explicit
va rog

Answer 1

$\it |x+1|( |2x+1| - 5) \ \textless \ 0\ \ \ \ (1)$

$\it |x+1| \geq 0\ \ \ \ (2)$

$\it (1), (2) \Longrightarrow x+1 \ne 0 \Longrightarrow x \ne -1 \ \ \ \ (3)$


[tex]\it |2x+1|-5 \ \textless \ 0 \Leftrightarrow |2x+1| \ \textless \ 5 \Leftrightarrow -5\ \textless \ 2x+1\ \textless \ 5|_{-1} \Leftrightarrow \\ \\ \Leftrightarrow -6\ \textless \ 2x\ \textless \ 4|_{:2} \Leftrightarrow -3 \ \textless \ x \ \textless \ 2 \ \ \ \ (4) \\ \\ (3), (4) \Longrightarrow S=(-3, -1) \cup (-1, 2) \\ \\ \it S \cap\ \mathbb{Z} = \{ \it -2, 0, 1\}[/tex]