Question -
Answer -
We know that, if we take reciprocal of any inequality we need to change the inequality as well.
Also, |x| – 3 ≠ 0
|x| > 3 or |x| < 3
For |x| < 3
–3 < x < 3
x ∈ (–3, 3) …. (1)
The equation can be re–written as
|x| – 3 > 2
Let us add 3 on both the sides, we get
|x| – 3 + 3 > 2 + 3
|x| > 5
Let ‘a’ be a fixed real number. Then,
|x | > a ⟺ x < –a or x > a
Here, a = 5
x < –5 or x > 5 …. (2)
From (1) and (2)
x ∈ (–∞,–5 ) or x ∈ (5, ∞)
∴ x ∈ (–∞,–5 ) ⋃ (–3, 3) ⋃ (5, ∞)