Question

Determinați Mulțimea A={x€Z/ |2x-1|_<2}

Answer 1

$A=\{x\in\mathcal{Z}\mid \ \ \mid2x-1\mid\textless\ 2\}\\\\Explicitam \ modulul:\\\mid2x-1\mid= 2x-1 \ daca \ x\geq \frac{1}{2} \\\mid2x-1\mid=-2x+1 \ daca \ x\leq \frac{1}{2}\\Tu \ ai \ nevoie \ de \ o \ valoare \ a \ modulului \ mai \ mica \ ca \ 2.\\Atribuind\ valori\ arbitrare\ lui\ din\ cele\ 2\ intervale\ gasite\ mai\ sus\ putem\ deduce\ ca\ pentru\ ca\\\mid2x-1\mid \ sa\ fie\ mai\ mic\ ca\ 2\ dar\ totusi\ pozitiv\ x\ va\ lua\ valori\ de\ la\ \\-\frac{1}{2}\ pana\ la\ \frac{1}{2}$

$x\in{[-\frac{1}{2}, \frac{1}{2}]}$