Question

|1-x|< 5 решается так? 1-x< 5 1-x-5=0 -4-x=0 x=4 если неправильно, то решить.

Answer 1

$|t|\ \textless \ a\; \; \; \Rightarrow \; \; \; -a\ \textless \ t\ \textless \ a\\\\\\|1-x|\ \textless \ 5\; \; \; \Rightarrow \; \; \; -5\ \textless \ 1-x\ \textless \ 5\; \; \Rightarrow \; \; \; \left \{ {{1-x\ \textless \ 5} \atop {1-x\ \textgreater \ -5}} \right. \\\\ \left \{ {{1-5\ \textless \ x} \atop {1+5\ \textgreater \ x}} \right.\; \left \{ {{x\ \textgreater \ -4} \atop {x\ \textless \ 6}} \right. \; \; \Rightarrow \; \; \; -4\ \textless \ x\ \textless \ 6\\\\x\in (-4,6)$