The solution of the inequality x+7x−5+3x+12≥0 is

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[1,3]∪(5,∞)

(1,3)∪(5,∞)

(−∞,1)∪(5,∞)

none of these

answer is A.

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Detailed Solution

We have x+7x−5+3x+12≥0⇒ 2x+14+3x2−14x−52(x−5)≥0⇒ 3x2−12x+92(x−5)≥0⇒ (x−1)(x−3)(x−5)≥0From the sign scheme, x∈[1,3]∪(5,∞)

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