Question

Решеть неравенства: а) ι х-5 ι ≤2 б) ι x+1ι > 5

Answer 1

$a)\; \; |x-5| \leq 2\; \; \to \; \; \; -2 \leq x-5 \leq 2\; ,\; 3 \leq x \leq 7\\\\b)\; \; |x+1|\ \textgreater \ 5\; \; \to \; \; \left [ {{x+1\ \textgreater \ 5} \atop {x+1\ \textless \ -5}} \right. \; \; \left [ {{x\ \textgreater \ 4} \atop {x\ \textless \ -6}} \right. \\\\\\//////(-6)----(4)/////\\\\P.S.\; \; |x|\ \textless \ a\; \; \Rightarrow \; \; \; -a\ \textless \ x\ \textless \ a\; \; \; \; ---(-a)/////(a)---\\\\|x|\ \textgreater \ a\; \; \Rightarrow \; \; \left [ {{x\ \textgreater \ a} \atop {x\ \textless \ -a}} \right. \; \; \; \; /////(-a)---(a)/////$