Solve x(x-7)(x-9)<0 and express the solution set in interval notation.

Question

A. (–infinity, 0)
B. (–infinity, 0) U (7, 9)
C. (–infinity, 0) U (9, infinity)
D. (–infinity, 9)

Answer 1

It is a cubic, with three real zeroes (0,+7 and +9), therefore the graph crosses the x-axis three times.
The coefficicent of the x³ term is positive, so it increases to the right of the largest root (+9) and decreases to the left of the smallest root (0).
This tells us that (-∞,0) is a subset of the solution.
To find the remaining part of the solution, we note that the function is positive between 0 and the next root, and dips below zero again between the last two roots, namely +7 and +9.
Thus the missing interval is (7,9).
Can you take it from here?

Answer 2

Based upon your explanation, I am goin to say the answer is

B(–infinity, 0) U (7, 9)

? Is this correct?

Answer 3

Correct!