x2 – 5x + 6 > 0 ⇒ (x – 3) (x – 2) > 0.
The critical points are 3 and 2.
Plotting 2 and 3 on the number line, we have it as shown below:
The number line is divided into three parts. Now we examine the sign of the expression (x – 3) (x – 2) in each of these three intervals.
As (x – 3) (x – 2) > 0, the points 2 and 3 are included here.
When x < 2, (x – 3) (x – 2) > 0 ⇒ x∈ (– ∞, 2]
When x > 3, (x – 3) (x – 2) > 0 ⇒ x∈ [3, ∞)
When 2 < x < 3, (x – 3) (x – 2) < 0
∴ x∈ (– ∞, 2] ∪ [3, ∞)
