Question Number 108987 by bobhans last updated on 20/Aug/20
Answered by bemath last updated on 20/Aug/20
$$\:\:\:\:\frac{\mathcal{B}{e}\mathcal{M}{ath}}{\blacksquare\mathcal{C}\square\square\mathcal{L}\blacksquare} \\ $$$${because}\:\mid{x}−\mathrm{3}\mid\:+\:\mathrm{2}\:>\:\mathrm{0}\:{for}\:{x}\:\in\:\mathbb{R} \\ $$$${then}\:\mathrm{3}−\mid{x}−\mathrm{3}\mid\:<\:\mathrm{4}\mid{x}−\mathrm{3}\mid\:+\:\mathrm{8} \\ $$$$\Rightarrow−\mathrm{5}\mid{x}−\mathrm{3}\mid\:<\:\mathrm{5}\: \\ $$$$\Rightarrow\mid{x}−\mathrm{3}\mid\:>\:−\mathrm{2}\:\Rightarrow\:\forall{x}\in\mathbb{R} \\ $$