Find the solution set of the inequation < 0. x ≠ 2

means we have to find values of x for which is negative

Observe that the numerator |x – 2| is always positive because of mod, hence for to be a negative quantity the denominator (x – 2) has to be negative

That is x – 2 should be less than 0

⇒ x – 2 < 0

⇒ x < 2

Hence x should be less than 2 for

x < 2 means x can take values from -∞ to 2 hence x ∈ (-∞, 2)

Hence the solution set for is (-∞, 2)