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Question
Solve `1/(|2x - 1|) < 6` and express the solution using the interval notation
Solution
`1/(|2x - 1|) < 6`
⇒ `|2x- 1| > 1/6`
⇒ `2x - 1 > 1/6`
`2x > 1/6 + 1 (= 5/6)`
⇒ `x > 5/12` ......(1)
or
`2x - 1 < 1/6`
`2x < 1/6 + 1 (= 7/6)`
⇒ `x < 7/12` ......(2)
From (1) and (2)
⇒ `5/12 < x < 7/12`
(i.e.) `x ∈ (- ∞, 5/12) ∪ (7/12, ∞)`
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