If (x + 3)(x - 5) > 0, then find the range of x.
Explanation:
Given, (x + 3)(x – 5) > 0
The given inequality is possible when
Case 1: Both (x + 3) and (x – 5) are positive i.e., x + 3 > 0 ⇒ x > -3 …(1) x – 5 > 0 ⇒ x > 5 …(2)
From (1) and (2) x > 5 …(3)
Case 2: Both (x + 3) and (x – 5) are negative i.e., x + 3 < 0 ⇒ x < -3 …(4) x – 5 < 0 ⇒ x < 5 …(5)
From (1) and (2) x < -3 …(6)
From (3) and (6), we get -3 > x > 5
i.e., x ∈ (-∞, -3) ∪ (5, ∞)
Hence, option (c).
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