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ED1.5.61Give,in interval notation, the unknown numbers Ihe following descrpbon_ When IS added lo twice number; the result is greater than equalto 13Selecl Ihe conec...

Question

ED1.5.61Give,in interval notation, the unknown numbers Ihe following descrpbon_ When IS added lo twice number; the result is greater than equalto 13Selecl Ihe conect choice below and, necessary: fill in Ihe answer box lo complete your choice-0 A: The solution sel iS (Simplify your answer Type your answer interval notation ) The solulion set is 0Click l0 select and enter ) Quf answeris) and then click Check AnswerAII parts showing

ED 1.5.61 Give,in interval notation, the unknown numbers Ihe following descrpbon_ When IS added lo twice number; the result is greater than equalto 13 Selecl Ihe conect choice below and, necessary: fill in Ihe answer box lo complete your choice- 0 A: The solution sel iS (Simplify your answer Type your answer interval notation ) The solulion set is 0 Click l0 select and enter ) Quf answeris) and then click Check Answer AII parts showing



Answers

Solve. Write the solution set using interval notation. See Examples 1 through 7.
$$
13 y-(9 y+2) \leq 5(y-6)+10
$$

All right. So if you try solve the absolute value, all the absolute value of three X is greater than 12. What you're gonna do is we're gonna take a value inside that circle. You the three acts, drop the absolute value, and you're gonna set that equal to possibilities. So it's one possibility is that three X is a positive value, right? People too, are riskier than a positive value. So you sleep. This is a positive 12. So if it's a positive just gonna be exactly what the relationship already is as it already exists, so three x s period than 12. The other possibility is that theon positive what's actually there? So we could say that three X is not greater than but because it's the opposite. We're going to do the opposite and all the end, the opposite of the value. So is the relation. Three X is less than the opposite of 12 which is negative. So here your two possibilities, we solve them just like we always saw the nanite Pahlavi. So how do you undo times by three Divided by three both sides. We get X is greater than four and the other one on New Times by three. Divide by three books. Signs ending in X is less than negative for so the two possibilities here the excess career than for an excess. Also less than negative for so on a number line appear weaken. Graph it. So we can say that X has to be greater than four unless the negative for So let's just put a negative for here. And this could count by force here basically, so we every had the lines going for value. So we're gonna see that. That's what forces zero, and that's one of the four that's positive. Okay, so it's access greater than four doesn't include, for that's all that used greater than for an excess less than negative for So it doesn't include for, But it's all night used that are less than listen negative forces. So here's your answer Exes, all things that are less than they get it for. And also all things that are greater than positive for that makes sense, because if you put a negative five in there, you're gonna get a true statement right three times, and I get If I wasn't, I get 15 negative 15 absolute values. Positive team, which was better than 12. Right, So it works now. How did write this sanitation for this You'd write? Basically, this situation acts. This is a set of all X is such that. And then you'd write X is basically going to be between, so we'll split the excellent middle. Um, exes. So the sanitation we had the set of all X such that X is greater than four or exes less than negative. For if you were doing the interval notation, what you're gonna do is you're gonna ask yourself, uh, what's the smallest and largest OK value. So we're looking at this left hand side here because either the smallest value is negative Infinity. So I get in on Saturday, and that means that it's gonna be a open fronts. Easier bracket will be closed like has a defendant went the open parentheses basically means that it has no defended important because affinities don't have any differently than when you guys go further torture infinity and negative or positive. So it's gonna be negative, Henry, with the breath sees on the left hand side, that's the smallest. And then the largest is gonna be negative for right so comma I get it for and it doesn't include negative four. So you putting up in practice sees this ball right. That's just not including the negative for. And then you would put a little you here, that's like basically, Or And then you do the other one and the other one is that the smallest value is perhaps used. That doesn't include for but for and then comma was the largest value, and this would be positive, right? So that's awesome. Repo pregnancies guys, if any counter to be a little bigger and you never know where that definitively ends, So this would be your interval notation to be your sanitation.

Inequality involving the absolute value and committing. Does that your ex minister Ni needs between the 13 and minus thing and then we will at knife, it's Scient. You removed the nine and we should get Listen with your ex and the media and the two side hand will be granted to It isn't gonna Manus far. And the next time we will be by everything here by Jew. And then we get the eggs and the middle between 11 and the manis Jew, and this will be the answer we can read his answer in the interval notation will be some honest juju 11.

All right. When solving this absolute value, all the you've already isolated unit all be. Now we can see here that absolutely of three x to spare the nape of zero. Which basically means that, um if you were Teoh, think about visitor possible here. Right? Uh, you two possibilities when you take away this absolute value parts the three X is greater than zero. What you see is what you got and that the opposite That is true. So that three X is worth the opposite. What you thought, Which means that incident birth unable to its and says nearly the opposite 00 is its own opposite. So that's just a zero. So now we're looking at a situation where we have three access, barely able to zero. Anthrax is also less than able zero. Well, I think that we can start to see exactly what that's gonna be if we divide everything by three. You see, that X is greater than Michael. Zero actual is also over here less than or equal to zero. So we're looking at all the things greater than any or all the things that are less than or equal to zero on There's a little bit of over a lot of time for both people, Cyril. Right? So this is basically everything right? It's all things that are that exists. Um, and let's see if that makes sense, right? If you were to put a negative one for axe three times a negative one is negative. Three is the absolute value of negative three. There's a yes, three is for the ankle. Zero. You put a positive one here. You also get three. It's fair that those Oh, so it looks like this is gonna be a situation where everything is true, right? So it's an or they're going in opposite directions. They both started zero. All right, so basically, you're looking at an end point of zero, so it's included, but two different intervals, right? Everything that isn eight, infinity to zero. And then everything that's from Seo two pops. Positive affinity. So that's what you're really looking at. The graph The interval notation for this would be that you have an open ended in point negative insanity and you have a closed and 0.0. Then you have and closed in 0.0. An open ended and point at possible city. So really, this is what we're talking about. Yes, you could You could technically, right. This as negative infinity to positive energy open and other signs as an alternative that there's already, uh, because they've been in the same thing, right? It goes every value that assists. So over here at the sanitation, you right, the set of all access. Such that, uh, company the quality. Yeah. This is gonna be an hour or so. It's gonna be none. Come down. So you can write this as such. That X is greater than or equal to zero or access less than equals zero. That's it. On a simple way of saying this is, um, real numbers. Uh huh.

All right, So we're solving the absolute inequality to explain his three is greater than able to. You're gonna remove the absolute value sign, and you're gonna take the inside value. You're gonna set two possibilities up. One possibility is that exactly what you see, what you get two X minus three is greater than or equal to two. The other possibility is that the opposite is true. That two X minus three is not greater than people too, but less than are able to not positive but negative. And when you said the other possibility of the opposite possibility is really like you take this one on the left and use multiply by negative What? I would be the same idea, right? So it's either that value or relationship or the officer that rushed. And now we saw both of these scenarios. So the way you're gonna do that is you want to get the X by itself, you're gonna add freed about signs and the results is on the left relationship you get to acts is better than reports of five on the right relationship. You get to acts is less than able to one, and then you're gonna divide both sides by two. And both processes solved for either one of these inequalities, as you wanted. Not that invite of two excellent value of one acts and they get X is greater than or equal to five. House. She was 2.5. And on the other side over here, you get acts is less than or equal to 1/2 which is just half. Yeah, So it makes sense to use the interval of 1/2. We do our graph. We're gonna go try graph. We're gonna count by one house, uniquely one happen to 1/2. So I just start with zero, and then it got one to three. So that means that this is 2.5 and that this is what? Okay? And now you're going to but close dots, because this includes value you as endpoints, right? Because that's where they're equal to or less than people to. So that means we're gonna have a close dot at 2.5, and we're gonna close dot at on half now. It's all the body is greater than 2.5 in less than 1/2 which means this is not going towards job. They're going away from each other through this is not an end. This isn't or relationship, right? So there's two scenarios, right? All the values that are less than 1/2 for work and all of the guys that are greater than 2.5 4 or able to. And so I wanna make sure we highlight that there. So this is what your graph will look like when you know if your graph, you're gonna write your solution set in sanitation. So that would be the set of all X is such that X is less than or equal to 1/2 or axe is greater than or equal to 2.5. Okay, when you're doing the interval notation que intervals that relate to one another. Both of them have parentheses on the outside, right, so that these princes there's from negative infinity. So this first interval here on the left is from negative ended two pots to positive 1/2. So the native affinity is a parentheses because I thought that we have no descended on point, but we have 1/2 which is a definitive that point. So when we have the greatest value. That suit that interval being 1/2 you could put a bracket on that side. Okay, so the Francis telling you it's opening on less than us. All aside and then on the greater than the greatest side. We've got 1/2 as a finite at, and then we're gonna put a you between the two, Then 2.5 is the beginning point. Smallest value. It is a definitive end points of a bracket and then 2.5. And then the largest value is positive. Any of course, which is going to be possible eternity and positive. Infinity is going to have a parentheses because there's no definitive and the positive. In other words, you can always make it a little bigger, right? So that's why there's no bracket on that side. That's it. That's idea. From


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