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CGP EDU Academic Team
Published on: August 14, 2026
The complete solution set of the inequality (|x – 1| – 3) (|x + 2| – 5) < 0 is (a, b) ∪ (c, d) then the value of |a| + |b| + |c| + |d| is
Text Solution
Verified by ExpertsThe correct answer is:
C
(|x – 1| – 3) (|x + 2| – 5) < 0
Case-I: x ≤ – 2
(x + 2) (x + 7) < 0 ⇒ x ∈ (–7, –2) .......(i)
Case-II : – 2 < x ≤ 1
(x – 4) (–x – 2) < 0 ⇒ (x – 4) (x + 2) > 0
⇒ x ∈ (– ∞ , –2) ∪ (4, ∞ )
No solution
Case-III x > 1
(x – 4) (x – 3) < 0
x ∈ (3, 4) .........(ii)
x ∈ (i) ∪ (ii) ⇒ x ∈ (–7, –2) ∪ (3, 4)
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