Question

Solve |x| < 4, when x ϵ R.

Answer 1

|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)