∣∣x∣+2x∣≤3, interval x=...? A.−3≤x≤3 B. x≥0 C. x≤0 D. −1≤x≤1 E. x≤2


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Question Number 10973 by ridwan balatif last updated on 05/Mar/17

$∣∣ x ∣ + 2 x ∣⩽ 3, interval x = . . . ?$ $A . - 3 ⩽ x ⩽ 3$ $B . x ⩾ 0$ $C . x ⩽ 0$ $D . - 1 ⩽ x ⩽ 1$ $E . x ⩽ 2$
Commented by ajfour last updated on 05/Mar/17

$D .$ $W h e n x ⩾ 0, ∣∣ x ∣ + 2 x ∣=∣ 3 x ∣ = 3 x$ $w h i l e w h e n x ⩽ 0, t h e s a m e i s ∣ - x + 2 x ∣$ $= ∣ x ∣ = - x .$ $s o t h e e n t i r e r a n g e i s - 3 ⩽ x ⩽ 1 .$ $. . a s c a n b e v i e w e d i n t h e g r a p h b e l o w .$
	Answered by ajfour last updated on 05/Mar/17

	Commented by ridwan balatif last updated on 05/Mar/17

	$thank you sir$
	Answered by sandy_suhendra last updated on 05/Mar/17

	$if x ⩾ 0 \Rightarrow ∣ x + 2 x ∣⩽ 3$ $∣ 3 x ∣⩽ 3$ $∣ x ∣⩽ 1 \Rightarrow - 1 ⩽ x ⩽ 1$ $so 0 ⩽ x ⩽ 1 . . . (1)$ $if x < 0 \Rightarrow ∣ x - 2 x ∣⩽ 3$ $∣ - x ∣⩽ 3 \Rightarrow - 3 ⩽ x ⩽ 3$ $so - 3 ⩽ x < 0 . . . (2)$ $from (1) \cup (2) = {- 3 ⩽ x ⩽ 1}$ $we can choose D$
	Commented by ridwan balatif last updated on 05/Mar/17

	$thank you sir$
	Answered by Mechas88 last updated on 06/Mar/17

	$- 3 ⩽∣ x ∣ + 2 x ⩽ 3$ $- 3 ⩽ 3 x ⩽ 3$ $- 1 ⩽ x ⩽ 1$ $x ⩽ 1$ $x ⩾ - 1$ $R t a D$
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