Answer: [tex]\bold{\dfrac{3}{2}<x<5\quad \rightarrow \quad \text{Interval Notation}: \bigg(\dfrac{3}{2},5\bigg)}[/tex]
Step-by-step explanation:
First, factor the inequality and solve for x to find the zeros.
Then, choose test points on the outside of those values and between them.
Plug them in to determine which one(s) yield a negative (< 0).
2x² - 13x + 15 < 0
(2x - 3)(x - 5) < 0
2x - 3 = 0 and x - 5 = 0
x = 3/2 and x = 5
I choose the left test point of 0 (2(0) - 3) × (0 - 5) > 0 (+)
I choose the between test point of 2 (2(2) - 3) × (2 - 5) < 0 (-)
I choose the right test point of 6 (2(6) - 3) × (6 - 5) > 0 (+)
Illustration of Graph:
+ --- +
←----|----------o----------------|---------------o--------------|----→
0 3/2 2 5 6
Since the "between" test point is the only one that yielded a negative, then the solution is the values between 3/2 and 5.
