So we're being asked to graph the following inequalities on the number one. So let's start with example number one. So the first thing is to understand what the inequality is saying. So let's read it. Well, it says X is greater than negative three. Meaning we wanna shade all the values of X that are greater than negative three. Remember, the first thing you have to ask yourself is, Should you have an open circle or a close? Circle it Negative three, in other words, is negative. Three A solution. Well, is negative three greater than negative three. Well, no, this would be false, which means that we're going to have an open circle. So negative three. We're gonna have an open circle. Now we have to determine, should we shade to the right or to the left of our circle? Well, we're talking about all the values of X is greater than negative three. So that would be like negative 1157 And all these values are to the right of negative three. So on our number line, we're going to shade all to the right off our original circle at negative three, because again thes air all the possible values of X that could be potential solutions to our inequality and again go all the way to the arrow there. So now we have graft a number line to represent the solution set for X is greater than negative three. Now let's take a look at number two. So aren't the quality, says X is less than or equal to five. So the first thing we have to determine is should we have an open or closed circle? It five. Well is five less than or equal to five? Yes, it ISS five is less than or equal to five because it's equal to it, which means we have a true statement, which means five is including our solution set. Therefore, we're gonna have a close circle it five. Now we have to determine should we shade to the right or to the left of thought? Well, all the values that are less than or equal to five are to the left of it, because some examples would be like 310 negative three etcetera. So on our number line, we're going to shade all the values of acts that are less than five again. Essentially, we're shading our number line everywhere to the left. And like I said before, I typically make my arrow larger. So that way, just to indicate that I'm shading everything to the lab and now we have graft both of our inequalities.

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## Video Transcript

So we're being asked to graph the following inequalities on the number one. So let's start with example number one. So the first thing is to understand what the inequality is saying. So let's read it. Well, it says X is greater than negative three. Meaning we wanna shade all the values of X that are greater than negative three. Remember, the first thing you have to ask yourself is, Should you have an open circle or a close? Circle it Negative three, in other words, is negative. Three A solution. Well, is negative three greater than negative three. Well, no, this would be false, which means that we're going to have an open circle. So negative three. We're gonna have an open circle. Now we have to determine, should we shade to the right or to the left of our circle? Well, we're talking about all the values of X is greater than negative three. So that would be like negative 1157 And all these values are to the right of negative three. So on our number line, we're going to shade all to the right off our original circle at negative three, because again thes air all the possible values of X that could be potential solutions to our inequality and again go all the way to the arrow there. So now we have graft a number line to represent the solution set for X is greater than negative three. Now let's take a look at number two. So aren't the quality, says X is less than or equal to five. So the first thing we have to determine is should we have an open or closed circle? It five. Well is five less than or equal to five? Yes, it ISS five is less than or equal to five because it's equal to it, which means we have a true statement, which means five is including our solution set. Therefore, we're gonna have a close circle it five. Now we have to determine should we shade to the right or to the left of thought? Well, all the values that are less than or equal to five are to the left of it, because some examples would be like 310 negative three etcetera. So on our number line, we're going to shade all the values of acts that are less than five again. Essentially, we're shading our number line everywhere to the left. And like I said before, I typically make my arrow larger. So that way, just to indicate that I'm shading everything to the lab and now we have graft both of our inequalities.

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