x-2x-3-interval-x-A-3-x-3-B-x-0-C-x-0-D-1-x-1-E-x-2-

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

∣∣ x ∣ + 2 x ∣⩽ 3, interval x = \dots ?

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 \dots (1)

if x < 0 \Rightarrow ∣ x - 2 x ∣⩽ 3

∣ - x ∣⩽ 3 \Rightarrow - 3 ⩽ x ⩽ 3

so - 3 ⩽ x < 0 \dots (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

Facebook Tweet Pin