00:01
Whereas to solve the non -linear inequality, 3x plus 12 over x minus 1 is less than 0.
00:07
The first step in solving a rational inequality like this would be to find the zeros of both the numerator and denominator.
00:16
The numerator gives me a 0 of x equals negative 4, and the denominator gives me a 0 of x equals 1.
00:26
Now i'm going to use those zeros to separate or partition the number line into intervals.
00:30
The zeros of the numerator and denominator are also known as critical values.
00:35
In this case, the two critical values divide the number line into three distinct intervals.
00:43
The next step is to pick a number in every interval and evaluate it back into the original rational inequality, determine if it's a true or false statement.
00:51
A true statement would mean that the interval is part of the solution.
00:54
Otherwise, it's not.
00:57
So from the first interval, i've chosen the value negative 5.
01:01
So i'm going to plug negative 5 back in here and see if you.
01:03
It is a solution or true solution to this inequality.
01:14
Simplifying there gives us that one half is less than zero, which is not true.
01:19
So that tells us that the first interval does not satisfy our inequality.
01:31
When we test a value in the second interval, which i chose zero, we get that negative 12 is less than zero, which is a true statement, which means that the second interval contains all correct values of this inequality...
