Question

Solve `1/(|2x - 1|) < 6` and express the solution using the interval notation

Answer 1

`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, ∞)`