Question Number 227236 by AlanMuhamad last updated on 09/Jan/26
![∣x−1∣≥6 x−1≥6 or x−1≤−6 x≥7 x≤−5 s_1 =[7,+∞) s_2 =(−∞,−5] s=(−∞,−5] U [7,+∞) R/(−5 , 7 )](https://www.tinkutara.com/question/Q227236.png)
$$\mid{x}−\mathrm{1}\mid\geqslant\mathrm{6} \\ $$$${x}−\mathrm{1}\geqslant\mathrm{6}\:\:\:\:\:{or}\:\:\:\:\:{x}−\mathrm{1}\leqslant−\mathrm{6} \\ $$$${x}\geqslant\mathrm{7}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{x}\leqslant−\mathrm{5} \\ $$$${s}_{\mathrm{1}} =\left[\mathrm{7},+\infty\right)\:\:\:\:\:\:\:\:{s}_{\mathrm{2}} =\left(−\infty,−\mathrm{5}\right] \\ $$$${s}=\left(−\infty,−\mathrm{5}\right]\:{U}\:\left[\mathrm{7},+\infty\right) \\ $$$${R}/\left(−\mathrm{5}\:,\:\mathrm{7}\:\right) \\ $$