Question Number 192570 by mechanics last updated on 21/May/23
Answered by cortano12 last updated on 21/May/23
$$\:\mid\mathrm{x}^{\mathrm{2}} −\mathrm{4}\mid<\mathrm{5} \\ $$$$\:\left(\mathrm{x}^{\mathrm{2}} −\mathrm{9}\right)\left(\mathrm{x}^{\mathrm{2}} +\mathrm{1}\right)<\mathrm{0} \\ $$$$\:\left(\mathrm{x}+\mathrm{3}\right)\left(\mathrm{x}−\mathrm{3}\right)\left(\mathrm{x}^{\mathrm{2}} +\mathrm{1}\right)<\mathrm{0} \\ $$$$\:\:\therefore\:−\mathrm{3}\:<\:\mathrm{x}\:<\:\mathrm{3}\: \\ $$
Answered by Skabetix last updated on 21/May/23
$$\mid{x}\mid+\mid{x}+\mathrm{2}\mid+\mid\mathrm{2}−{x}\mid\leqslant\mathrm{8}\Rightarrow−\frac{\mathrm{8}}{\mathrm{3}}\leqslant{x}\leqslant\frac{\mathrm{8}}{\mathrm{3}} \\ $$