okay, in this example, we're being asked to solve the given compound in the quality, and then we're gonna graph the solution set on the number line. Well, no, this that it's one compound inequality all at once. This is AnAnd Statement. So our goal is to get X all by itself in between the two outside numbers. So the way you go ahead and solve this is just like you normally would. The first time we have to do is move the seven. So to do this, we're going to subtract seven from each side of our inequality from the left, the middle and the right. Well, let's start on the far left. We have one minus seven, which is negative. Six we'll bring down are less under equal to sign. Now. In the middle, we have seven minus seven, which is zero those canceled. So we just have negative two X again, we'll bring down our next inequality sign, and then we have nine minus seven, which is two. Okay, so now how do we get X by itself? Well, we would get X by itself by dividing each side by negative too. Now, don't forget we're dividing inequality by a negative, which means that both of our inequality signs they're going to flip. So we're gonna have negative six divided by negative two, which is positive three. Now we're gonna flip part inequality side around, so we'll have greater than or equal to in the middle the negative choose cancel. So we just have X again, we're gonna flip part in the quality sign because we divided by a negative. Now we have to develop by negative two, which is negative one. So what we found for our compound in the quality we have three is greater than equal to X, which is greater than negative one. Now, typically, when you have compound inequalities in this fashion, you always put the smallest value first. So in this case, essentially what we're going to dio is we're gonna flip this whole thing around. Someone do that we're gonna have negative one is less than next, which is less than or equal to three. So notice how both in the qualities end up flipping back. Okay, Perfect. Now we want to go ahead and graft us on the number line so we'll set up our number line. We'll put our two key values negative one and three at negative one will have an open circle because X is greater than negative one not equal to it. And that three will have a close circle because X could potentially be 33 is part of our solution set. So notice how exes in between, negative one and three. So we just need to shade in between negative one and three. So now we have solved and graft to given compound inequality. And again the same rule applies anytime you divided inequality by a negative, the inequality signs still needs to flip around.

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## Video Transcript

okay, in this example, we're being asked to solve the given compound in the quality, and then we're gonna graph the solution set on the number line. Well, no, this that it's one compound inequality all at once. This is AnAnd Statement. So our goal is to get X all by itself in between the two outside numbers. So the way you go ahead and solve this is just like you normally would. The first time we have to do is move the seven. So to do this, we're going to subtract seven from each side of our inequality from the left, the middle and the right. Well, let's start on the far left. We have one minus seven, which is negative. Six we'll bring down are less under equal to sign. Now. In the middle, we have seven minus seven, which is zero those canceled. So we just have negative two X again, we'll bring down our next inequality sign, and then we have nine minus seven, which is two. Okay, so now how do we get X by itself? Well, we would get X by itself by dividing each side by negative too. Now, don't forget we're dividing inequality by a negative, which means that both of our inequality signs they're going to flip. So we're gonna have negative six divided by negative two, which is positive three. Now we're gonna flip part inequality side around, so we'll have greater than or equal to in the middle the negative choose cancel. So we just have X again, we're gonna flip part in the quality sign because we divided by a negative. Now we have to develop by negative two, which is negative one. So what we found for our compound in the quality we have three is greater than equal to X, which is greater than negative one. Now, typically, when you have compound inequalities in this fashion, you always put the smallest value first. So in this case, essentially what we're going to dio is we're gonna flip this whole thing around. Someone do that we're gonna have negative one is less than next, which is less than or equal to three. So notice how both in the qualities end up flipping back. Okay, Perfect. Now we want to go ahead and graft us on the number line so we'll set up our number line. We'll put our two key values negative one and three at negative one will have an open circle because X is greater than negative one not equal to it. And that three will have a close circle because X could potentially be 33 is part of our solution set. So notice how exes in between, negative one and three. So we just need to shade in between negative one and three. So now we have solved and graft to given compound inequality. And again the same rule applies anytime you divided inequality by a negative, the inequality signs still needs to flip around.

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