The values of x which satisfied $|3x|≥|6-3x|$
A. (0, 1]
B. [1, 4]
C. (4, ∞)
D. (-1, 0)
E. (-∞, 0)
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → B and C only
$|3x|≥|6-3x|$
$⇒|3x|-|6-3x|≥0$
Case 1: $-∞<x<0$
$-(3x)+(6-3x)≥0$
$-3x+6-3x≥0$
$-6x+6≥0$
$-6x≥-6$
$x≥1$
Case 2: $0≤x<2$
$3x+6-3x≥0$
$6≥0$
Case 3: $x≥2$
$3x-6+3x≥0$
$6x-6≥0$
$6x≥6$
$x≥1$
$∴(4,∞),[1,4]$