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, ∞)