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The solution set of the inequality ∣3x∣≥∣6−3x∣|3 x| \geq|6-3 x| is :

Solution

✅ Correct Option: 2

Case 1: x≥2x \geq 2

∣6−3x∣=3x−6|6-3x| = 3x-6

The inequality becomes: ∣3x∣≥3x−6|3x| \geq 3x-6

Since x≥2x \geq 2, we have ∣3x∣=3x|3x| = 3x

So: 3x≥3x−63x \geq 3x-6, which is always true when x≥2x \geq 2


Case 2: 0≤x<20 \leq x < 2

3x≥03x \geq 0 and 6−3x>06-3x > 0

The inequality becomes: 3x≥6−3x3x \geq 6-3x

Solving: 6x≥66x \geq 6, so x≥1x \geq 1

This gives us: 1≤x<21 \leq x < 2


Case 3: x<0x < 0

3x<03x < 0 and 6−3x>06-3x > 0

The inequality becomes: −3x≥6−3x-3x \geq 6-3x

Simplifying: 0≥60 \geq 6 (false)

No solutions here.

Combining all cases, the solution set is: x≥1x \geq 1

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