Question

Care este solutia inecuatiei: |x-1|(|2x-1|-5)<0 stiind ca x apartine lui Z*

Answer 1

$Cum~|x-1| \geq 0~rezulta~|2x-1|-5\ \textless \ 0. \\ \\ |2x-1|-5\ \textless \ 0 \\ \\ |2x-1|\ \textless \ 5 \Rightarrow -5\ \textless \ 2x-1\ \textless \ 5 \\ \\ -5\ \textless \ 2x-1\ \textless \ 5~~~~~~~~~~~~~~|+1 \\ \\ -4\ \textless \ 2x\ \textless \ 6~~~~~~~~~~~~~~~~~~~|:2 \\ \\ -2\ \textless \ x\ \textless \ 3,~x \in Z \Rightarrow x \in \{-1,0,1,2\}. \\ \\ \underline{Solutie}:~x \in \{-1;-0;1;2 \}.$