write-the-solution-set-of-each-inequality-if-x-is-an-element-of-the-set-of-integers-x2-4-x40

Question

Write the solution set of each inequality if x is an element of the set of integers.
$x^{2}-4 x+4>0$

Bahar Tehranipoor · Accepted Answer

and this question. We want to write the solution, set up each inequality if X is an element in the centre manager. So here we have extreme minus four rifles for greater than zero. So first, let&#x27;s factor this factor. Extra miles four. It was four. We know that the constant four. We&#x27;re gonna look at it and find the multiples that will equal for so that sounded kind of convoluted. But what I mean is what numbers will most likely get? Four. We have four and 12 and two. And so what combination to have to use, we&#x27;re gonna have to use fact that negative two squares four so that we have X minus two squared is how we factor this. Because then we would have X squared minus two x minus two X, which gives us minus four X and then minus two times minus two, is positive for no one to say. This is great in zero. So let&#x27;s find that factor, which is X equals two. That&#x27;s where we have zero and we use a little number line. So put two right there. So let&#x27;s pick a value above two and see what we get If we pick something like three and plug it in, we get a positive number. So that works. And if we pick something below to, like a negative number negative three, we plugged it in. That also works. And the easiest way to know this is because if something is square, it&#x27;s always me positive. So basically four X that is any numbers we could say ex lesson to X ray than two, except for X equals to, because that would give us zero. And that is not what the inequalities asking for all these real numbers of suffer, too, will satisfy this inequality.

M S · Answer

so we have X squared minus four. X plus four is greater than equal to zero. So first we need to factor left hand stop splitting apart this middle turn. So we took our coefficient and multiply our last time and we get positive court. Then we know any our numbers to add to negative for So melissa factors a 41 and four and two and two and they both even need to be positive or both either need to be negative. In this case, they both need to be negative because we want them add to negative for So now we&#x27;ve picked our pair negative to minus two because I&#x27;d give us negative for I still have X squared minus two. It&#x27;s my Sue IX plus four. So a group the first to thank you for a second to and from the 1st 1 with background It&#x27;s still have X minus two from the second we factor out of negative too. So we have X minus two. So because this term matches this term, we know that our factories are X minus two times X minus two scarier than zero. So because this is an inequality, we take further steps to solve for the range of excess. Then, if we just said equal to zero when it&#x27;s just said equal to zero, we just have one answer. But now we&#x27;re looking for a range of answers. So we know that a positive times a positive begin this a positive. We also need to consider that a negative times negative, but give us a positive. So I need to solve using these rules so we&#x27;ll have X minus two is greater than zero and X minus. Two is going to be zero. Get in April tube. We also need to say X minus two. It&#x27;s Liston. Include a zero and X minus. Two is less. Danny, what is here? So the positive. That just means greater than equal to. And the positive just means good, unequal to. And the only reason we said things that we split them apart is because we need to combined their results. What are we gonna get? A positive answer. I want to add to the both sides here. We&#x27;ll have eggs. Good. Any Put it to the same thing Here. Thanks is greater than equal due to so John limber line that we have to, and it&#x27;s gonna go this way. Could scar deviant. So does have exes. Great. Any older too. You also need to saw looky here. So I&#x27;m gonna add to the both sides we exist by standing equal due to, you know, the same thing here X is less than equal to two. So, John, I&#x27;m relying. Starting it, too. We&#x27;re gonna go less than it. So X is less than are able to to. So because they don&#x27;t have any common area, we&#x27;re going to use the word or not. And so we&#x27;re gonna have the word or in between the two, cause there&#x27;s no common girl. We also need to find a solution set that just means we need to find a a couple of numbers us around our range someone, a job brackets and some dots to show that it&#x27;s a list. And it&#x27;s not just these four numbers, because we&#x27;re again. We&#x27;re looking for a range of values, so I always go to below are Lois number. So too low, too is zero and one in this case, too, because we have less than or equal to two. So we can include two in this list I always go to above our highest number in his case is still too. So huh? Three and four. And the one includes more dots because the list is not in there. And now we have a solution. Is that?

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.

Bahar Tehranipoor · Answer

in this exercise, we want to bite the solution. Sentence inequality. So let&#x27;s factor extra minus two x Easy thing to do to take out a next. So we have X Times X minus two. Screaming Eagle zero. Now let&#x27;s find the values of except Make this inequality zero and that will be at zero and two. Now let&#x27;s use our trusty number line. So zero to and I was just testing values that are greater than two between your own too, and in less than zero. So if we pick a number over to like three, what will we get? We&#x27;ll get a positive number three times three minus two, which is positive, which is in fact, greater than zero. So we can say that yes, this region works. Let&#x27;s pick one in betweens your own to like. One will do. One times one minus two, which is a negative numbers to this region does not work. And then we can pick a value less than zero like negative one. Plug that and we get a negative times negative, which is in fact, Raylan zero. So you can say this region works, so we also know that zero into themselves will work because we&#x27;re saying greater than or equal to zero. So we can say that X that is less than or equal to zero will give us the solution and then X, that is greater than or equal to two will give us a solution, and that is all there is to it.

Bahar Tehranipoor · Answer

this question. We want to solve this inequality. So did you. No. Let&#x27;s first factor. Expert plus X minus 12. You know, we&#x27;re gonna have to look at the multiple 12 which are six and 23 and four to factor this and knowing that three and four have one difference between each other that will help us get this X that we can just do X plus four times X minus three as then we&#x27;ll have X squared minus three X plus four x, which is X in the minus 12. Mrs. Listen zero. So we have that. The critical values here X equals negative four in x 63 Let&#x27;s use our number line. So on our number line we will put negative for put three. So it&#x27;s picked values above three betweennegative four and three and then below negative for So if you pick one over three like four will have a positive times of positive and that will not work for us. So we cannot use this region that we pick one in between negative four and three like zero for you. Zero. We have a positive and a negative, which is less than zero. So this region does work. And then if we pick one below negative four, like negative five, we get a negative number of times the negative number, which is positive. So this region does not work. So our solution is only between negative four and three. So you can say that X is between you before three. That&#x27;s it.

Bahar Tehranipoor · Answer

and this exercise. We want to write the solution set of this inequality. If X is an element of the set of imagers, so first thing we want to do is just factor to X squared minus two x minus 24. I think the easiest thing to do is take a two out of there first. So we take it to out. We have two times X squared, minus eggs, minus 12. This is still a coarse grade zero. Now, how do we factor expert minus X minus 12? Now, if we look at that, we&#x27;re just trying to find factors of 12. So there&#x27;s six and 23 and four and thinking about three and four. We know that there&#x27;s one difference between them. So if we can factor using three and four to get this negative X term, that would be a way to do it. So here we have X next. So we have a negative X. We want a negative four. I&#x27;m in a blustery because then we would have X squared minus four X plus three x O Negative X and then minus 12. When we can&#x27;t forget that too greater than zero. So Now what values of this expression here make it zero. That&#x27;s going to be negative. Three and four. So now what we&#x27;re going to do is we&#x27;re going to use a little number line here. So we have the values Negative three and four. So protective three. And therefore now the way toe. See what our solutions that is, is we pick values over four in between a three and four and less than negative three and see if they satisfy our inequality. So let&#x27;s pick a value over for, like, five. What happens if we plug in five into this? So we get five foot three, which is positive five minus four, which is positive and two. So all those numbers will fly together. We get a positive number so we can say yes. Numbers over four will give us a solution that makes inequality troop stricken number between negative three and four. And I think the easiest one do to you is just zero plugging zero. We get zero procedures positive zero minus four, which is negative. And then, too, of course it was positive. So here we have a negative number, So numbers in between do not work. Now let&#x27;s pick a number between, uh, negative infinity night of three. So just proximately negative for you. Go back. Negative. Four plus three is in negative number. Negative. Four minus four is negative numbers or negative times. Negative is positive times too, Which is positive. So numbers below negative three to work. People that agreed. Yeah. So our solution set is now going to be ex Less than negative. Three and X is greater than four. That&#x27;s it.

Problem

Write the solution set of each inequality if x is…

Problem 13 Easy Difficulty

Write the solution set of each inequality if x is an element of the set of integers.
$x^{2}-4 x+4>0$

Answer

$\{x | x<2 \text { or } x>2\},\{\ldots, 0,1,3,4, \ldots\}$

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Ann Xavier Gantert

Algebra 2 and Trigonometry

Grace H.

Catherine R.

Caleb E.

Maria G.

Absolute Value - Example 1

Absolute Value - Example 2

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$\{x | x<2 \text { or } x>2\},\{\ldots, 0,1,3,4, \ldots\}$

Algebra 2 and Trigonometry

Grace H.

Catherine R.

Caleb E.

Maria G.

Absolute Value - Example 1

Absolute Value - Example 2

Ann Xavier GantertAlgebra 2 and Trigonometry

Grace H.

Catherine R.

Caleb E.

Maria G.

Ann Xavier Gantert

Algebra 2 and Trigonometry