CUET Preparation Today
If $|3x|≥|6-3x|, x\in R,$ then x lies in |
[0, ∞) [1, ∞) [4, ∞) [-1, ∞) |
[1, ∞) |
The correct answer is Option (2) → [1, ∞) $|3x|≥|6-3x|$ ($|3x| → (I), |6-3x| → (II)$) $⇒|3x|-|6-3x|≥0$
Case 1: $x<0$ $-3x+6-3x≥0$ $-6x≥-6$ $x≥+1$ → not possible Case 2: $0≤x<2 $3x+6-3x≥0$ $6≥0$ Not possible Case 3: $x≥2$ $3x-6+3x≥0$ $6x-6≥0$ $x≥1$ $x∈[1, ∞)$ |
