Question

Solve the inequality (x² - 4)(x² - 5x + 6) > 0 and express the solution in interval notation.

A) (-[infinity], 2) ∪ (3, [infinity])
B) (-[infinity], 2) ∪ (2, 3) ∪ (3, [infinity])
C) (-[infinity], 2) ∪ (2, 3)
D) (-[infinity], 2) ∪ (3, 5) ∪ (5, [infinity])

Answer 1

To solve the inequality (x² - 4)(x² - 5x + 6) > 0, we find the values of x that make each factor equal to zero, and then determine the intervals where the inequality is true. The solution in interval notation is (-[infinity], -2) ∪ (2, 3) ∪ (3, [infinity]).

Step-by-step explanation:

To solve the inequality (x² - 4)(x² - 5x + 6) > 0, we first find the values of x that make each factor equal to zero: x² - 4 = 0 and x² - 5x + 6 = 0. Solving these equations, we find that x = -2, 2, 3. So, the inequality is true when x is less than -2 or between 2 and 3, or greater than 3.

Expressing the solution in interval notation:

• (-[infinity], -2) ∪ (2, 3) ∪ (3, [infinity])