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:

B and C only

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: $x≥2$

$3x-6+3x≥0$

$6x-6≥0$

$6x≥6$

$x≥1$

$∴(4,∞),[1,4]$