The set of integers that satisfies 5>∣n−2∣≥∣n+1∣ is


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Question Number 33468 by NECx last updated on 17/Apr/18

$T h e s e t o f i n t e g e r s t h a t s a t i s f i e s$ $5 >∣ n - 2 ∣⩾∣ n + 1 ∣ i s$
	Answered by MJS last updated on 17/Apr/18
	$25>(n−2)^2 n^2 −4n−21<0 n=2±(√(25))=2±5 ⇒ n∈]−3;7[ (n−2)^2 ≥(n+1)^2 6n≤3 n≤(1/2) ⇒ n∈]−∞;0] ]−3;7[ ∩ ]−∞;0]=]−3;0] ⇒ ⇒ n∈{−2; −1; 0}$
	$25 > {(n - 2)}^{2}$ $n^{2} - 4 n - 21 < 0$ $n = 2 \pm \sqrt{25} = 2 \pm 5 \Rightarrow n \in] - 3; 7 [$ ${(n - 2)}^{2} ⩾ {(n + 1)}^{2}$ $6 n ⩽ 3$ $n ⩽ \frac{1}{2} \Rightarrow n \in] - \infty; 0]$ $] - 3; 7 [\cap] - \infty; 0] =] - 3; 0] \Rightarrow$ $\Rightarrow n \in {- 2; - 1; 0}$
	Commented byNECx last updated on 17/Apr/18

	$w o w . . . . . l o t s o f t h a n k s s i r . I^{'} m ⊛$ $m o s t g r a t e f u l .$
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