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Solve the inequation \(\bigg|\frac{2}{x-4}\bigg|\) >1, x ≠ 4.

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  \(\bigg|\frac{2}{x-4}\bigg|\) >1, x ≠ 4

⇒ \(\frac{2}{|x-4|}>1\)  ⇒ 2 > | \(x\) – 4 | ⇒ | \(x\) – 4 | < 2

⇒ 4 – 2 < \(x\) < 4 + 2 ⇒ 2 < \(x\) < 6        [|\(x\) – a| < r ⇒ a – r < \(x\) < a + r]

But \(x\) ≠ 4 

∴ x∈ (2, 4) ∪ (4, 6)

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