Question Number 8262 by 666225 last updated on 04/Oct/16
$$\mid{x}−\mathrm{1}\mid\:<\:\mathrm{2}\:\Rightarrow\:\mid{x}−\mathrm{3}\mid \\ $$
Commented by 123456 last updated on 04/Oct/16
$$\mid{x}−\mathrm{1}\mid<\mathrm{2}\Leftrightarrow−\mathrm{2}<{x}−\mathrm{1}<\mathrm{2} \\ $$$$−\mathrm{2}−\mathrm{2}<{x}−\mathrm{3}<\mathrm{2}−\mathrm{2} \\ $$$$−\mathrm{4}<{x}−\mathrm{3}<\mathrm{0} \\ $$$$\mathrm{0}<\mid{x}−\mathrm{3}\mid<\mathrm{4} \\ $$