Problem

Solve each inequality, and graph the solution set…

02:39

Problem 6 Easy Difficulty

Solve each inequality, and graph the solution set.
$$
(x+6)(x-2)>0
$$

Answer

Related Courses

Precalculus

Algebra

Beginning and Intermediate Algebra

Chapter 11

Quadratic Equations, Inequalities, and Functions

Section 8

Polynomial and Rational Inequalities

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Video Transcript

All right, we have X plus six times X minus two, and that is greater than zero. So, typically, when we're solving a quadratic inequality, we would factor. This one's already factored for us. So at this point, we treat this like it's an equation. We let each factor equal zero. So if X Plus six is equal to zero than X, must be negative sex. There's one of our roots. And if x minus two is equal to zero, then you get X equals two. There's another route. Now we wanted to solve and graft the solution set. I'm actually going to use the graph to help determine this solution set, because here's what happens. We know when we look at our number line, we're gonna have a value and negative six. We're gonna have another one. It too. And I wanted to know when this function was greater than zero not greater than or equal to. So these are going to be the end points of our interval, but they're not gonna be included as part of the solution set. So I'm gonna have open circles there. They just indicate where the intervals end or begin. But they're not included. Now, at this point, what I want to do is throwing a test value kind of see which way my solution sets going. Because we know when we're doing quadratic inequalities, our solutions that will either be everything in between our two routes or everything to the left of the first route and right of the second route. It doesn't always happen, but usually that's the way this goes. So I want to test value. Okay, Um and if I'm either gonna be between him or on either side, If I test something that's in between here, I usually pick something convenient. Like in this case, I would pick zero. Then I'll know which way my solution sets going. So if I test X equals zero, I'm gonna plug zero win and see if it checks. That's going to give me zero plus six time zero minus two. And I want to see if that's bigger than zero. Well, that's gonna give us six times negative too, which is negative. 12 negative. 12 is clearly not greater than zero. So that fails. That means X equals zero is not part of our solution Set that indicates to me then that are intervals are gonna be the left of negative six until the right of to Which means our solution sent is the interval from negative infinity Negative six or from two to infinity.

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