Question 178782: Solve.
(x+13)(x-6)(x+5)>0
Use at least one inequality or compound inequality to express your answer. For answers with more than one inequality, separate the inequalities by a comma.
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
First determine the three values that would make the expression on the left equal to zero, namely: -13, -5, and 6
Plot these three points on the number line and notice that you have partitioned the number line into 4 regions.
and 
Note that all of the inequality signs exclude equals because if x were equal to any of the three values, the value of the expression would be zero and the relation greater than zero would fail.
Now, from each of the four regions, select a value. It doesn't matter what value, as long as it is in the specified interval and does not equal one of the partition points.
First, select something in the interval , say -15. If -15 is substituted for x in the original inequality, the relationship fails because all three factors will be negative making the left side negative and therfore not greater than zero. This interval is excluded from the solution set.
Select something in the interval , say -10. If -10 is substituted for x, then  ,  , and  . One positive factor and two negative factors means the product is positive and therefore greater than zero. This interval is included in the solution set.
Using the same process to discover that is excluded and and is included.
Solution set: 
Below is a graph of (x - 6)(x + 5)) . Note the portions of the graph that are above the x-axis.
|
|
|
