x| > 4 Square
⇒ x 2 > 16
⇒ x 2 – 16 > 0
⇒ x 2 – 4 2 > 0
⇒ (x + 4)(x – 4) > 0
Observe that when x is greater than 4, (x + 4)(x – 4) is positive
And for each root the sign changes hence
We want greater than 0 that is positive part
Hence x should be less than -4 and greater than 4 for (x + 4)(x – 4) to be positive
x less than -4 means x is from negative infinity to -4 and x greater than 4 means x is from 4 to infinity
Hence x ∈ (-∞, -4) and x ∈ (4, ∞)
Hence the solution set of |x| > 4 is (-∞, -4) U (4, ∞)