Как решать такие неравенства с модулями?2|x| больше 1/2

[latex]2|x|\ \textgreater \ \frac{1}{2}\\\\|x|\ \textgreater \ \frac{1}{4}\\\\x\ \textgreater \ \frac{1}{4}\; \; \; ili\; \; \; x\ \textless \ -\frac{1}{4}\; \; \; \to \; \; \; \left [ {{x\ \textgreater \ \frac{1}{4}} \atop {x\ \textless \ -\frac{1}{4}}} \right. \\\\x\in (-\infty ,-\frac{1}{4})\cup (\frac{1}{4},+\infty )\\\\\\P.S.\; \; \; 1)\; \; |x|\ \textgreater \ a\; \; \to \; \; \; \left [ {{x\ \textgreater \ a} \atop {x\ \textless \ -a}} \right. \\\\ ///////(-a)-----(a)///////\\\\2)\; \; |x|\ \textless \ a\; \; \; \to \; \; \; -a\ \textless \ x\ \textless \ a\; \; \to \left \{ {{x\ \textless \ a} \atop {x\ \textgreater \ -a}} \right. \\\\------(-a)\; ///////\; (a)------[/latex]