Solution:
We already know that when we take the reciprocal of any inequality, we must also change the inequality.
Also, |x| – 3 ≠ 0
This implies that : |x| > 3 or |x| < 3
Now, For |x| < 3
–3 < x < 3
x ∈ (–3, 3) …. (1)
We can re-write this equation as
|x| – 3 > 2
Adding 3 on both the sides, we get:
|x| – 3 + 3 > 2 + 3
|x| > 5
Consider to ‘a’ be a fixed real number. Then, we have;
|x | > a ⟺ x < –a or x > a
Here, we have a = 5
x < –5 or x > 5 …. (2)
Using (1) and (2), we get:
x ∈ (–∞,–5 ) or x ∈ (5, ∞)
∴ x ∈ (–∞,–5 ) ⋃ (–3, 3) ⋃ (5, ∞)