Question Number 155393 by cortano last updated on 30/Sep/21
$$\:\:\mid\mid\mathrm{x}−\mathrm{4}\mid−\mathrm{4}\mid\:\geqslant\:\mathrm{4}\: \\ $$
Answered by mr W last updated on 30/Sep/21
$$\mid{x}−\mathrm{4}\mid−\mathrm{4}\geqslant\mathrm{4}\: \\ $$$$\Rightarrow\mid{x}−\mathrm{4}\mid\geqslant\mathrm{8}\: \\ $$$$\Rightarrow{x}−\mathrm{4}\geqslant\mathrm{8}\:{or}\:{x}−\mathrm{4}\leqslant−\mathrm{8}\: \\ $$$$\Rightarrow{x}\geqslant\mathrm{12}\:{or}\:{x}\leqslant−\mathrm{4} \\ $$$${or} \\ $$$$\mid{x}−\mathrm{4}\mid−\mathrm{4}\leqslant−\mathrm{4}\: \\ $$$$\Rightarrow\mid{x}−\mathrm{4}\mid\leqslant\mathrm{0}\: \\ $$$$\Rightarrow{x}=\mathrm{4} \\ $$$$ \\ $$$${solution}: \\ $$$${x}\leqslant−\mathrm{4},\:{x}=\mathrm{4}\:{or}\:{x}\geqslant\mathrm{12} \\ $$