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Question Number 114593 by abdullahquwatan last updated on 19/Sep/20
((∣x−1∣)/(∣x∣−1)) ≤ 1
∣x−1∣∣x∣−1⩽1
Answered by MJS_new last updated on 19/Sep/20
(1) ∣x∣−1≠0 ⇒ x≠±1 (2) ∣x∣−1<0 ⇒ −1<x<1 ∣x−1∣≥∣x∣−1 true ∀x∈R ⇒ −1<x<1 (3) ∣x∣−1>0 ⇒ x<−1∨x>1 ∣x−1∣≤∣x∣−1 true for x≥1 ⇒ x>1 ⇒ −1<x<1∨x>1
(1)∣x∣−1≠0⇒x≠±1(2)∣x∣−1<0⇒−1<x<1∣x−1∣⩾∣x∣−1true∀x∈R⇒−1<x<1(3)∣x∣−1>0⇒x<−1∨x>1∣x−1∣⩽∣x∣−1trueforx⩾1⇒x>1⇒−1<x<1∨x>1
Commented by abdullahquwatan last updated on 20/Sep/20
thanks sir
thankssir

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