|x| < 4

Square

⇒ x² < 16

⇒ x² – 16 < 0

⇒ x² – 4² < 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 less than 0 that is negative part

Hence x should be between -4 and 4 for (x + 4)(x – 4) to be negative

Hence x ∈ (-4, 4)

Hence the solution set of |x| < 4 is (-4, 4)