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A = {\(x\) :11\(x\) - 5 > 7\(x\) + 3, \(x\) ∈ R} and  

B = {\(x\) : 18\(x\) – 9 > 15 + 12\(x\), \(x\) ∈ R}.

The range of the set A ∩ B is 

(a) [– ∞, 4]

(b) (0, 4) 

(c) [4, ∞] 

(d) (– 4, 4)

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(c) [4, ∞)

A = {\(x\) : 11\(x\) – 5 > 7\(x\) + 3, \(x\) ∈ R} 

⇒ 11\(x\) – 5 > 7\(x\) + 3     ⇒ 4\(x\) > 8 ⇒ \(x\) > 2 

⇒ A = {\(x\) : \(x\) > 2, \(x\) ∈ R} 

B = {\(x\) : 18\(x\) – 9 > 15 + 12\(x\), \(x\) ∈ R} 

⇒ 18\(x\) – 9 > 15 + 12\(x\) ⇒ 6\(x\) > 24 ⇒ \(x\) >

⇒ B = {\(x\) : \(x\) > 4, \(x\) ∈ R} 

∴ A ∩ B = {\(x\) : \(x\) > 2, \(x\) ∈ R} ∩ {\(x\) : \(x\) > 4, \(x\) ∈ R} 

\(x\) > 4 ⇒ x∈ [4, ∞).

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