In Exercises 1–26, graph each inequality. x≤−3

Question

Accepted Answer

Hey everyone welcome back in this problem. We are asked to graph the following inequality and we're giving X is less than or equal to negative. Let's go down to the bottom. Just give ourselves some more room to work. Rewriting what we were given X is less than or equal to negative. Now when we have an inequality like this and we're asked to graph it. The first thing we wanna do is graph the equality. Okay so we're gonna change that inequality sign to an equality and we're gonna graph X is equal to negative eight. Now X is equal to negative eight. We know that that's gonna be a vertical line. Okay, A vertical line at that X. Value of -8. So let's draw this, This is gonna be -8. We're gonna have a vertical line there. Now the question is do we draw this line as a solid line indicating that we're including negative eight? Or do we draw it as a dashed or dotted line indicating that we aren't including the value of X equals negative eight. Well in our inequality we have X is less than or equal to negative eight because we have that equal negative eight. We can have X equals negative eight. So we draw it as a solid line because we can include it. So we draw X Is equal to -8. This line here. And let me just I'm gonna draw this in blue. So it's easier to make out the difference between that and our axis. Alright so we have the the line X is equal to negative eight here and now. The question is, what side of this line do we include? Okay, so this line kind of creates a boundary between two parts of the plane and we need to figure out which part of the plane is included in our inequality. So we have X less than or equal to negative eight. So what we want is we want X values that are smaller than negative eight. Where do we have X values that are less than negatively. Well, that's going to be to the left Of this line, to the left of -8 in our graph. So to the left of the line is going to be included. Now if you were stuck and you couldn't figure out whether we should be including this, the left side or the right side. What you can do is you can always test a particular point. So if you were to take a point, say X equals zero. Mhm Zero less than or equal to negative eight. No it's not, zero is not less than negative eight is greater than negative eight. Which means that that point isn't included. So we know that the right hand side wouldn't be included and you can do the same thing on the left side. If you take a point negative 10, that is less than or equal to negative eight. So that means it's included. It satisfies that inequality. So we're including the left side. Okay, so you can always test points if you get stuck on that. Alright, so this is our diagram. Let's go back up to our answer choices and see which one we have. Now. We know that our boundary was a vertical line, so we can already eliminate C. And D. Because those are horizontal lines, and we want to include everything to the left of that boundary line of X equals negative eight. And so we're looking at option B. Thanks everyone for watching. I hope this video helped see you in the next one.