write-the-solution-set-of-each-inequality-if-x-is-an-element-of-the-set-of-integers-x2-x-60

Question

Write the solution set of each inequality if x is an element of the set of integers.
$x^{2}-x-6<0$

Bahar Tehranipoor · Accepted Answer

in this exercise, we want to write the solution set of this inequality. If X is an element in the set of injures, so first thing we want to do is just factor Expert minus X minus six. The easiest way to do this is look at the factors of six. So already we can see we have six and one. We have two and three. And you think six. Someone probably won&#x27;t give us our answer here. Because if we multiply six and won and we think about it in terms of factoring, we&#x27;re gonna either gets have been like five X or my seven X. It&#x27;s not gonna work using three and two. We&#x27;re probably going to end up with this negative X term so we can have X minus three times explodes, too, because if we well, by that out we get X squared plus two x minus three x, which gives us this negative X minus six. This is less than zero. Let me see that are critical. Values are at X equals three and X equals negative to Celeste drawer number one drawing a number line. We have three and negative too. So first we want to pick some values above three and then in between negative two and three and then below negative to plug them in and see what we get. So if we plug in a number above three, like four of them and we get four minus three, which is a positive number and four plus two, which is a positive number, positive times positive gives you a positive value. And of course, that is not less than zero. So we say that this region does not work. Now, if we pick something in between negative two and three like zero, we plug that and we get a native number times a positive, which just give us less than zero. So this region right here does work? No. If we pick something below negative to, like negative three, if you plug that in, we get a negative times negative, which will give us a positive value. So this region does not work. So, looking at a number line, we can see that the only reason that does work is when X is between negative, too, and three. And that&#x27;s your answer.

M S · Answer

so we have X squared minus X is less than six. So because we know you want a factor of China mule, we need to move this six to the other side. So I&#x27;m going to subtract six from both sides, so we&#x27;ll have X squared minus X minus six is less than zero. So the factor this we need to split apart or middle term here. So needles apart coefficient times our last term and not give us negative six. And we need them to add two neg newborn. So when a list of factors of 616 and two and three and we know that we need one of the numbers and prepare to be negative and also needs to add some negative boy. So after testing a lunch combinations will get positive, too, and negative. Three is our appeared. So now we just need to split apart of middle turn. So have X squared minus two x no plus two X minus three x and then one a six. Listen, zero throwing a group the first tooth and group the 2nd 2 So we&#x27;re gonna factor out the greatest common factor it from the person we get back here on exile, have X plus two you from the second we get back to what a negative three. So have explosives too, is gonna than zero and is listen zero Sorry. So because this is the same as this, we know that exposed to Times X minus three is less than zero. So solving inequalities takes a further step. Then just when the trying a mule&#x27;s equal to zero because we&#x27;re looking for a range of values. So we need to find arranged that meets all the qualifications. So because we know that this product is basically negative, less than zero means negative. The only way to get a negative product is if this one is positive and this one is negative, that would give us a negative, or this one is negative. And this one is positive, and I will also give us a negative. So I&#x27;m gonna say X plus two is positive. An X minus three is negative, and we also need to say X plus two isn&#x27;t a new an X minus three is positive. So when I say like, for instance, this one here, greater than zero just means it&#x27;s positive. So I just followed the signs. It really helps to do right down the signs under each factor. So that way you can make sure that she tests for all the possibilities. So no one is gonna sell critics. So subtract it from both sides. Will have X is greater than negative too. We added about sides here who have X is less than three. So we need to draw them. Relying it really hopes. No. A plot in ated to they will quite positive three. So know that X is greater than negative too. So to go this way and X is less than positive. Three. So this will go this way and we shade the combined area. It will have negative to this less than X is less than positive. Three for this one here we also need to solve for the other possibility. So over here you gotta subtract two from both sides. Say X is less than negative too. And here we&#x27;re at through to both sides will have X is greater than positive three. So when I draw another number light, you have negative too. And three. So it&#x27;s less than native to, and it&#x27;s greater than positive three. Now, there&#x27;s no common area to shade there, or this possibility does not exist. So we&#x27;re only gonna focus on this answer. We also need to find a solution set. That just means we&#x27;re gonna find about three or four numbers. The ex congee they&#x27;re always go to above and two below. So we&#x27;re gonna have brackets. I&#x27;m gonna start with some dots to show that it keeps going on. So two numbers below negative to that will be negative for negative three. And because we do not have a less standard equal to we cannot include negative, too. But we can start it positive three and two above three is or and five. And we also need to put some more dots to show that the range keeps going.

M S · Answer

So we have X squared by the six X plus. Bob is greater than zero. So first we need to factor left hand side so we don&#x27;t want them multiply too. Bye. Which is our coefficient times there last time, and we don&#x27;t want them to add to negative six. So let&#x27;s the practice of five, which is just one and five and about either need to be positive for both need to be negative. In this case, they&#x27;re both gonna need to be negative because of more than the after negative six. So this is our pair here, so I have X squared minus X minus, biopics in place spot. So group the 1st 2 and then give the 2nd 2 we&#x27;re gonna factor out. So benefactor on X here, so have excellent. It&#x27;s one. There was a factor out of negative five here will have Excellent. It&#x27;s going so because this time is the same as this term we found are two factors. So we have X minus one in X minus five is ready to zero. So because we&#x27;re dealing with any qualities, we want to find a range of values and not just one number that extra equal. Therefore, whenever we know that our product will be a positive number, we need to note that the positive times a positive well give us a positive number. But we also need to note that a negative times negative would give us a positive number. That&#x27;s what we need to solve for X minus Well, in times X minus five is less than zero because we need to find when it&#x27;s native cause it&#x27;ll still give. Give us a positive number, and that&#x27;s what garden zero means. It&#x27;s just positive number. It&#x27;s already said, say explosive Line X minus one is going to be zero, and that means X is greater than one. Then X minus five is guarded in zero, and you have five to both sides, so it is graded in five. It&#x27;s never gonna drawn and realize still have one here, and five here and X is greater than one. So to go this way and X is greater than five. So this will go this way, and we need to combine these two in the only way in Combined says the X is greater than five. Because I weigh it means both qualifications. We also need to solve Luca here. X minus one is less than zero and ext monos by his last thing. Zero so beyond one about side to you have excess less than one FBI popped. Both sides will have exits listed by So John. I could number line and kind of one, and by so it&#x27;s just less than one. So you know this way and X is less than five, so they don&#x27;t go this way. And the only way in these with qualifications as if X is less than one. So now we have our two ranges. And because they go opposite ways, the range is not in between one and by we have to use the word or or answer. We also need to find a solution set. That just means we&#x27;re gonna find that through four numbers that are ex congee. And we just want to write it in range for someone a right brackets and write some dots to show that there&#x27;s numbers before and there&#x27;s gonna be numbers after it, so always do to below our lowest number. In this case, it will be negative one and zero, and then I&#x27;ll do two numbers above our greatest number, which will be six and seven

M S · Answer

So we have X squared. Plus five X minus six is greater than zero. So the first thing we need to do is fact or love tea inside. So I&#x27;m gonna take our coefficient multiply bar. Last term, we get negative six and we know you wanted to add to our middle term, which is positive. Five. So now we list the package of 61 in six and two and three and we want to see which one. Well, at&#x27;s a positive by, but because our sixes negative, we know that one of the terms and appear must be negative. And after testing the lunch combinations, we&#x27;ll get negative one positive six. So now we&#x27;re gonna separate our middle time here, so we&#x27;ll have X squared, then minus xt plus six six and bring down in minus six. So they get the 1st 202nd too. And they were gonna back you&#x27;re out The greatest comic factor if when the 1st 1 will pull out on X and we&#x27;re left with X minus one and from the second little Kalata six and we&#x27;re left with x minus would And because this term here in this time here are the same. We know that we have our exit factors. So X minus one times the explicit six is greater than zero so that the weak factor it gets a little bit more complicated than that. When we just solved when it was said equal to zero because it&#x27;s an inequality, we must take a further steps. He find the range of values possible. So we know that a negative times negative give us a positive and a positive times. A positive would give us a positive. So because we want a positive answer, we can also have next minus one Times X plus six less than zero. We can also solve for that because a negative times in negative is a positive and a positive times. A positive is positive. So that&#x27;s how we consol for both of these. So when I started the one over on the left side, so have I. X minus one is guarded in zero and explicit. Six is greater than zero. So we add one and we get X is greater than positive one. There was a truck six over here, and we get X is greater than negative six. So because this isn&#x27;t inequality. Think of it as a number line. So I think this is like negative six and X has to be greater than it. So it&#x27;s about here. I can&#x27;t think of this. I was born and X has to be great. And so to go here. But next has to meet both of these qualifications. And the only way it does is it. X is greater than one, so to combine these two will have X is greater than one, but that&#x27;s only one of them. Now we need to go to our right side and we&#x27;ll have X minus. One is less than zero, and express six is less than zero. So I&#x27;m gonna add one about sites, and we get X is less than one. And it was a track six on both sides, and we get X is less than negative. Six. Like I said, think about our number line. So we&#x27;ll have one here and as his lesson one. So have to go this way and we&#x27;ll have negative six here, and it&#x27;s ex has to be less than that, and the only way X meets both of these qualifications. As if X is less than six. If X is less than thanks like negative six. Sorry. So these are our two answers. X is greater than one and X is less than negative six.

Bahar Tehranipoor · Answer

in this exercise, we want to write The solution set of each to quality X is an element of the set of images. So we have X squared plus five X plus six is less than zero. So it&#x27;s factor this knowing we have a constant six year means. We have to look at the factors of six so free and two of six and one, and here we can use three into because we&#x27;ll have extra story. Times X plus two is less than zero. So are critical values of X equals negative three and negative too. So let&#x27;s draw our number line. You have negative three. We have negative too. Let&#x27;s pick values in each of these three regions, so pick something above negative too. We could just be like zero. We plug in zero, we will not get a negative numbers. This region very clearly does not work. Now we pick something between a three legged too, like negative 2.5 will get a positive times negative, which is less than zero. So this region does work. Now we pick something below negative three, like negative four will get a negative negative, which is positive. So this region does not work. Now we have exes between negative three and negative, too. But because this question is asking for access and element on the set of managers, you can see there&#x27;s actually no images that go between any 23 and go to because they&#x27;re not inclusive. We can&#x27;t use negative three negative, too, because plugging those and we&#x27;ll get zero. But we&#x27;re just looking for less than zero, so there&#x27;s actually no injures in this solution. Set satisfied inequality.

Bahar Tehranipoor · Answer

told this inequality and find the solution set. So here we want to dio is factor extra plus X minus two. So let&#x27;s do that. If we do that, we have these two terms of X. So if we have negative to really, the only thing we can factor that into is to win one. So let&#x27;s put it positive, too, and a negative one, because then we&#x27;ll have X squared plus two x minus X, which gives us this positive eggs minus two. This Quimby listen zero. So let&#x27;s find the values that make this expression zero that would be at X equals one and X equals negative, too. Now we&#x27;re going to use a number line. So our values were one and negative. To put one, I need to know to find the solution set. The easiest thing we could do is take values over one between negative two and one and then the load eight of two. So let&#x27;s start with over. One will pick something like two. We plug in to we get to minus one, which is a positive number, and then two plus two is a part of number, and that is not less than zero. So we will call back and say that this region does not work. Now let&#x27;s pick a number between eight of two and one like zero butt. Plug that and we get zero minus one, which is negative number negative 10 post to posit number two. Those numbers will be together or negative, which is less than zero. So that does in fact work. So this region is right. No, for pick something below native to like negative three. We get a negative number here and a negative number here. Multi together we get positive and that&#x27;s not less than zero. So this region does not work. So all in all our solution set is that X is going to be greater than negative too, but less than one. And that is our set.

Problem

Write the solution set of each inequality if x is…

Problem 7 Easy Difficulty

Write the solution set of each inequality if x is an element of the set of integers.
$x^{2}-x-6<0$

Answer

$\{x |-2<x<3\},\{-1,0,1,2\}$

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Ann Xavier Gantert

Algebra 2 and Trigonometry

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Absolute Value - Example 1

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$\{x |-2<x<3\},\{-1,0,1,2\}$

Algebra 2 and Trigonometry

Catherine R.

Heather Z.

Alayna H.

Kristen K.

Absolute Value - Example 1

Absolute Value - Example 2

Ann Xavier GantertAlgebra 2 and Trigonometry

Catherine R.

Heather Z.

Alayna H.

Kristen K.

Ann Xavier Gantert

Algebra 2 and Trigonometry