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x-1-lt-2-x-3-




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

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