Linear Inequations-15

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Solve the inequation:
|2/(x - 4)| > 1, x ≠ 4

Solution: We have,

|2/(x - 4)| > 1, x ≠ 4

=>2/|(x - 4)| > 1, [since, |a/b| = |a|/|b|]

=>2 > |x - 4| [since, |x - 4| > 0 for all x ≠ 4]

=> 4 – 2 < x < 4 + 2 [since, |x - a| < r <=> a – r < x < a + r]

=> 2 < x < 6

=> x ∈ (2, 6)

But, x ≠ 4.

Hence, the solution set of the given inequation is (2, 4) U (4, 6)

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