Published by:
CGP EDU Academic Team
Published on: August 13, 2026
The solution set of the inequality 
≥ 0 is
A
B
C
D
Text Solution
Verified by ExpertsThe correct answer is:
A
≥ 0 ⇒ 4 – x 3 > 0 ⇒ x 3 – 4 < 0 ⇒ x < 4 1/3 ...(i)
∴ |x + 2| – |x| ≥ 0
case-I : x ≤ –2 then –x – 2 + x ≥ 0 ⇒ –2 ≥ 0 no solution
case-II: –2 < x ≤ 0 then x + 2 + x ≥ 0 ⇒ x + 1 ≥ 0 ⇒ x ≥ –1
∴ x ∈ [–1, 0] ...(ii)
case-III : x > 0 then
x + 2 – x ≥ 0 ⇒ 2 ≥ 0 ∴ x ∈ R + ...(iii)
∴ (i) ∩ (ii) ∩ (iii) is x ∈ [–1, 4 1/3 ).
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