Certainly! I'd be happy to explain the question and help you understand the answer.
The given question is:
.
To solve this inequality, we need to determine the values of
for which the expression
is greater than zero (
).
To find the solution, we can use the concept of interval notation and zero-product property. Here's how we can proceed step by step:
1. Begin by finding the critical values of
where the expression changes sign. These occur when any of the factors are equal to zero. From the given equation, we have:



2. Now, we have four critical values:
,
,
, and
(since
yields
as well).
3. Plot these critical values on a number line:

4. Now, we need to test the expression
in the intervals created by these critical values. We will choose test points within each interval and determine if the expression is positive or negative.
For example, let's take a test point
from the interval
:

Since the expression
is positive in the interval
, this interval is part of the solution.
By repeating this process for the remaining intervals, you'll find that the complete solution to the given inequality is:

In interval notation, the solution is:


♥️
