So in this example, we're being asked to salt the given compound inequality and then we're gonna graft the solution set on the number one. So we have an and statement here and notice in this case that are to inequalities air separate. So what we're going to do first is solved. Both of our inequality separate. So let's start with our 1st 12 X minus three is less than or equal deny. So the solve for X, we're going to start by adding three to both sides of our inequality. So we're gonna be left with two X is less than or equal to well, nine plus three is 12 and then to get X by itself, we're going to divide both sides by two and 12. Divided by two is six. So we're gonna have X is less than or equal to six. Okay, now we have to go ahead and solve our second inequality. So to do this, I could start by subtracting five from both sides of our inequality. And we have eight minus five, which is three. So we're gonna have X divided by negative. Three is less than three. So now to solve for X. We need to multiply both sides of our inequality by our denominator there, which is negative. Three. But remember, when you multiply both sides of an inequality by a negative, you have to flip your inequality sign. So the lesson sign is going become a greater than sign. And then we have three times Negative three, which is negative. Nine. So now we've solved our compound inequality. We found that X is less than or equal to six and X is greater than negative nine. So we can write this as one inequality. So remember when the start with our smallest value, which is negative, nine. And we're gonna flip it around so it will become less than X. Then we'll have our next one we have X is less than or equal to six. So this could be how we can write our compound inequality as one statement. Okay, Now we're being asked to graft us on a number line, so we're going to set up our number line. We're gonna put negative nine and six on here. Those heirarchy values and negative nine, we're gonna have an open circle. Could it's negative. Nine is less than X, but it's six. We're gonna have a close circle because X is less than or equal to six. And because X is in between negative nine and six on our number line, we're going to shade in between negative nine and six. So now we have solved and graph the giving compound inequality.

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## Video Transcript

So in this example, we're being asked to salt the given compound inequality and then we're gonna graft the solution set on the number one. So we have an and statement here and notice in this case that are to inequalities air separate. So what we're going to do first is solved. Both of our inequality separate. So let's start with our 1st 12 X minus three is less than or equal deny. So the solve for X, we're going to start by adding three to both sides of our inequality. So we're gonna be left with two X is less than or equal to well, nine plus three is 12 and then to get X by itself, we're going to divide both sides by two and 12. Divided by two is six. So we're gonna have X is less than or equal to six. Okay, now we have to go ahead and solve our second inequality. So to do this, I could start by subtracting five from both sides of our inequality. And we have eight minus five, which is three. So we're gonna have X divided by negative. Three is less than three. So now to solve for X. We need to multiply both sides of our inequality by our denominator there, which is negative. Three. But remember, when you multiply both sides of an inequality by a negative, you have to flip your inequality sign. So the lesson sign is going become a greater than sign. And then we have three times Negative three, which is negative. Nine. So now we've solved our compound inequality. We found that X is less than or equal to six and X is greater than negative nine. So we can write this as one inequality. So remember when the start with our smallest value, which is negative, nine. And we're gonna flip it around so it will become less than X. Then we'll have our next one we have X is less than or equal to six. So this could be how we can write our compound inequality as one statement. Okay, Now we're being asked to graft us on a number line, so we're going to set up our number line. We're gonna put negative nine and six on here. Those heirarchy values and negative nine, we're gonna have an open circle. Could it's negative. Nine is less than X, but it's six. We're gonna have a close circle because X is less than or equal to six. And because X is in between negative nine and six on our number line, we're going to shade in between negative nine and six. So now we have solved and graph the giving compound inequality.

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