in-15-26-solve-each-inequality-and-write-the-solution-set-if-the-variable-is-an-element-of-the-set-6

Question

In $15-26,$ solve each inequality and write the solution set if the variable is an element of the set of integers.
$$
|2 b-7| \geq 9
$$

Joshua Utley · Accepted Answer

okay were asked to solve the following inequality. And we do that by splitting up are absolute value since it&#x27;s already isolated. So we have to be minus seven is greater than or equal to nine, and then we&#x27;re going to have to be minus seven less than minus nine. That&#x27;s a very and so here, we&#x27;re gonna solve both sides. So if I add seven here, nine plus seven is 16. So I have to be greater than or equal in 16 which gives me that B is greater than or equal to eight after a divide by two on both sides. And here I add seven to both sides again. And so I&#x27;m left to be less than or equal to minus two. And so B should be less than or equal to minus one. And so we can look and draw out our little number line real quick, and I have zero here. We have minus one here and out here we have eight. And so we need to check almost all of our points here just to make sure, because with this less than or equal sign, we need to make sure the core equals case works. So right now, leave open bubbles and minus one in eight, and we&#x27;ll test both of them. So if you buggin minus one to the original, you get minus two minus seven, which is greater than or equal than nine because it&#x27;s equal the nine. So that works. If you plug in eight, you get 16 minus seven absolute value, which is also equal to mine. So these work And then if I plug in a number less than minus one, say minus two, you would also get a number greater than or equal nine. So, like minus two, you get minus 11 in the absolute value. So this over here all works. If that bug in zero, you get zero minus seven, which doesn&#x27;t work. So this in here doesn&#x27;t work. And then if I plugged in 10 that would work. And so your solutions air drawn out here. And if you wanted a set for the integers, you would get a set of X in the integers Such that Okay, I&#x27;m sorry this had to be in the integers said be in the integers such that B is either greater than or equal to eight or B is less than or equal to minus one. It&#x27;s going to get a good grasp on when to use the word and or in this case it has to be one or the other. Obviously, you can&#x27;t be less than minus one and greater than eight at the same time. But there are cases where the board and is the correct word to use, but in this case it will be four.

Joshua Utley · Answer

All right. We&#x27;re asked to solve the absolute value in quality. We first isolate the inequality by adding six to both sides. And we have the final inequality we wanna work with. The absolute value of 11 minus to be is greater than 17. We split that into our two equations, 11 minus to be greater than 17 and 11 minus to be less than minus 70. And so, for both, we&#x27;re gonna subtract 11 from both sides and then divide by minus two. And so 17 minus 11 is going to give us six is we have minus to be greater than six. We divided by negative, too. So it since we divided by a negative, we have to flip our sign. So we have be less than minus three, and then we&#x27;re gonna do the same. Over here, minus 11 minus 11 minus 17. Minus 11 is minus 28. So you have minus to be less than minus 28. Divide by. Negative too. So we have to flip the sign again. Be is greater than 14. And so if we check this out zero here, 14 out here and minus three here. If we plug in minus five or something like that, something less than minus three, and we plug in minus five into let&#x27;s say, this equation. What we have is we have 11 plus 10 which is in the absolute value bigger than 17. So this works out and then four numbers bigger than 14. Let&#x27;s say 15. We have 11 minus 30 11. Minus 30 is 90 is minus 19 which in the absolute value is bigger than 17. So that works as well. The scent would be a set of all be elements of the integers such that B is either less than minus three or B is greater than 14 well.

Joshua Utley · Answer

all right, We&#x27;re asked to solve the absolute value inequality here, and we&#x27;re has to then put a set of solutions if any solutions are integers. And this is an interesting example because you could you could go about splitting up the equation and that would work for you. Um, I believe you&#x27;d get be greater than or equal to be less than or equal to two. But there&#x27;s a quicker way to look at this problem. You see, you have an absolute value here, and you have that that absolute value is greater than or equal to zero. And the absolute value is a distance. Basically eight plus four B. It&#x27;s a plus for bees, distance from zero. And so the absolute value is on Lee ever positive or it zero. And so when you say, hey, this absolute value is greater than or equal to zero. Well, yeah, for any BU plug in, that&#x27;s going to be true. And if you were to solve this, you would get something like B is less than or equal to two. I&#x27;m sorry B is greater than or equal to two, and B is less than or equal to. It would be something along those lines. And so what you end up with is you end up with this this solution that covers all the bees and it&#x27;s true if you plug in any be here, it doesn&#x27;t matter what it is. You&#x27;re going to get an answer that&#x27;s greater than zero. And if you plug in minus two, for instance, which would be the actual solution, you would just end up getting 00 is allowed since you have that or equals two part. So you&#x27;re set of solutions. Actually, his B and it&#x27;s just the set of all Be so we can say, for the set of integers, you can just say the set of solutions actually, for the integers is just the integers itself. Any inter jury you use works, okay? And so that would be the solution here

Aditya Sood · Answer

solved each inequality and write the solution said. If the variable is an element of the state of managers, So the inequality that were given is absolute value of people. Six is less than or equal to five. So what we can do here is that we can split this up into two parts we can make. This beeps of six is less than or equal to five, and it&#x27;s a B plus. Six is less than or equal to five, and the other part that we could make it is people sticks is greater than or equal to negative five. And so a next step will simply be to evaluate the equation. And so we can subtract six from both sides. To get B is less than or equal to make it a one and Andre inside, we can once against attracts six from both sides. To get B is clearly greater than or equal to negative 11. And so we can. Now we know that the solution set is going to be whatever is in between these two values, while including them too. So we can rewrite this in this notation, which states that the solution set is from negative 11 to negative one for all real imagers

Joshua Utley · Answer

all right, We&#x27;re asked to solve the absolute value inequality here, and we can do that by breaking it up into two separate equations. So the first equation makes sense, because if y plus two is greater than seven than the absolute value of Y, plus two is greater than seven. But also, if why plus two happens to be less than negative seven in the absolute value of Y, plus two will then be greater than seven as well. So this is how you&#x27;re gonna flip, do your inequalities. And so on the left side, you can subtract two from both sides. Why is greater than five? And on the right side you can get you could subtract two from both sides and get why less than negative nine. And so the best way to write out the solutions if you want to get a more comprehensive idea, is to draw a number line, and we will include the integers zero and one two. Anything doesn&#x27;t That&#x27;s a one. Then over here you have minus one minus two minus three minus for Carly contained this mother out minus five, minus six minus seven. And basically what they&#x27;re saying is this inequality is true. Whenever we use an open circle to tell you that minus seven isn&#x27;t included This inequality is true. When why is over here? And it&#x27;s also true. One why is over here? So they&#x27;re infinitely many integers that satisfy this. And if I was going to write that in some sort of sanitation, I would write that as the scent of why such that why is greater than five, or why is less than negative tonight, which is a mistake I made over here. This should be minus nine. And so there&#x27;s a pictorial representation of your solution. And so everything in here isn&#x27;t No, it wouldn&#x27;t work. But if you plug in anything bigger than five or less than minus nine, this absolute value inequality holds. And so this would be a set representation. And so they&#x27;re infinitely many managers in this solution.

Aditya Sood · Answer

solve each inequality and read the solution set. If the variable is an element off the set of managers, the inequality that we have been given is absolute value of X is greater than nine. So, uh, frankly, this doesn&#x27;t require too much math. Um, we know that the absolute value function uh, absolutely of X. It will take X and just make it positive. So if X is negative 10 it will simply make that positive benefits already positive. 10. You&#x27;ll keep that as positive 10. And so essentially, we just want to see for what may I use is x greater than, uh, nine. So, uh, did regardless f But regardless of sign. So whether it&#x27;s negative or positive, don&#x27;t care about the sangre schmancy for what values executed than mine. And so, um, we know that it&#x27;s going to be great tonight for value sections 10. 11. Doctor, I&#x27;ve got all the way up to infinity now, since this is absolute, this is this is absolute value. We also know that it will be greater than nine for our values, such as names of 10 you negative 11 all the way to negative infinity. And so, uh, we know that you want to know that this is not greater than on equal to or equal to. It is simply only clear then. So our domain is going to be from negative infinity to negative nine and nine to infinity. Ah, One thing to notice is that right here and right here that it is normal pregnancies that are being used, not square brackets such as these. Um, And the reason is because, uh, nine and negative night are not included within the solution set, so yes, thank you.

Problem

In $15-26,$ solve each inequality and write the s…

Problem 20 Hard Difficulty

In $15-26,$ solve each inequality and write the solution set if the variable is an element of the set of integers.
$$
|2 b-7| \geq 9
$$

Answer

$b \in(-\infty,-1] \cup[8, \infty)$

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Ann Xavier Gantert

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Absolute Value - Example 1

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$b \in(-\infty,-1] \cup[8, \infty)$

Algebra 2 and Trigonometry

Catherine R.

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Absolute Value - Example 1

Absolute Value - Example 2

Ann Xavier GantertAlgebra 2 and Trigonometry

Catherine R.

Heather Z.

Caleb E.

Kristen K.

Ann Xavier Gantert

Algebra 2 and Trigonometry