Solve each of the following system of equations in R.

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

⇒ xϵ (–3, 3) ….(1)

∴, The equation can be re–written as–

Adding 2 both the sides, we get–

|x|–3+3> 2+3

⇒ |x|>5

We know that,

|x |>a ⟺ x<–a or x>a

Here, a=5

⇒ x<–5 or x>5 ….(2)

⇒ x ϵ(–∞,–5 ) or x ϵ(5, ∞)

⇒ x ϵ(–∞,–5 ) ⋃ (–3, 3) ⋃ (5, ∞) (from 1 and 2)

We can verify the answers using graph as well.