Answer:
(3, 5 )
Step-by-step explanation:
Given that the intervals to be tested are
x < 3, 3 < x < 5, x > 5
Choose test points within each interval, evaluate and compare
For x < 3
Choose x = 0, thus
(0 - 3)(0 - 5) = (- 3)(- 5) = 15 > 0 ← solution not in this interval
For 3 < x < 5
Choose x = 4
(4 - 3)(4 - 5) = (1)(- 1) = - 1 < 0 ← solution in this interval
For x > 5
Choose x = 6
(6 - 3)(6 - 5) = (3)(1) = 3 > 0 ← solution not in this interval
Thus the solution to (x - 3)(x - 5) < 0 is
3 < x < 5, that is (3, 5)
