in-3-14-write-the-solution-set-of-each-equation-2-x-5213

Question

In $3-14,$ write the solution set of each equation.
$$
|2 x-5|+2=13
$$

Joshua Utley · Accepted Answer

all right, We&#x27;re us to solve the absolute value equation here we start by by isolating the absolute value. So I should have two X minus five is equal to 11 on. Then we split it into two equations. And then we saw. So I had five to this side. So I had to ecstasy with 16 which I then divide by two on each side and access E for the eight. And then here I had fired his world of assigned to excuse people from this time tumbling at six and then, after dividing like to X is equal to minus three. I can go ahead and check my solutions real quick by plugging your men so I should have for the 1st 1 16 minus five. I&#x27;m soon now. You must too, equals 13 16 minus five is 11 plus two is 13. So that works bunk in minus three. And I should get two times minus three, which is minus six minus five plus two years is 13 minus six times minus five. That&#x27;s the absolute value of minus 11. Lose two is 13 and so you have 11 plus two, Mr. So that one works as well. So your solution is that is that

Aditya Sood · Answer

everybody today we&#x27;re going to be solving absolute value of X minus five is equal to 12 and we&#x27;re going to find the solutions that for this equation. So a general rule to remember is that in order to solve the absolute value, often expression is equal to be we have to, uh, some divide this into two parts. Um, the two parts number one is a zero to be, and number two is a stable to negative B. So we&#x27;re gonna do a very similar thing right over here with this equation. So we get X minus five is equal to 12 af. After both science, we get X is equal to 17. So that&#x27;s one of her solutions. And our second solution is going to be X minus five is equal to negative 12 after after both eyes once again and we get exited with a negative seven and the&#x27;s are solutions

Aditya Sood · Answer

everybody. The question we&#x27;re going to do today is right. The solution set of each equation the equation were given is 35 minus this absolute value of 35 minus five X is it would attend. So the way we want to go about doing this is by subdividing this equation to two parts. So point number one is going to be 35 minutes, five exits, people positive can. In part two is going to be 35 minutes of X is equal in negative time. And this is what you want to do when you have inequalities when you&#x27;re dealing with the inequalities. So essentially, if, uh, this is absolute value of a is able to be, then you will always want to Sep Divide this into a is able to be and A is able to negativity. Yeah, that&#x27;s essentially what we&#x27;re doing here, too, is just this time over here and be just this term over here thinking over here. So now we just have to separate algebraic equations. We want to solve, uh, self for X. And so we subtract 35 from both sides over here, divide both sides by negative five and get executed. Five. That&#x27;s one of her solutions. And on the right equation, you want to subtract to defy from both sides and divide Grenada five to get X secret name and our solutions, that is right over here. X is equal to five and nine.

Aditya Sood · Answer

right, The solution set of each equation, but the question were given is absolute value of to a minus five. Is he? What? A seven. So we have this nice little method over here that when you have the absolute value of a is going to be we can subbed by this into two parts is about to be and a zero to negative B. And so that&#x27;s what we&#x27;re going to over here. Were given. Essentially, this is right over here is R A. And this is a B be on a and then what we&#x27;re gonna do is turn this into two equations and each equation will yield a separate solution. So, uh, number our first step, it&#x27;s going to be to a minus 50 to 7. So what does this one right over here and this is going to be the same as this one. And the second part is going to be to a menace obstacle to negative seven. So this right over here corresponds to this one, and now we&#x27;re just gonna further evaluate. So let&#x27;s start with the left hand side, left and equation. Uh, we&#x27;re going to add factor both sides, so we get to a 12 divide both sides by two, and we&#x27;re left with a 0 to 6. On the right hand side. We are gonna do a similar thing. We&#x27;re gonna act after what sides and divide by two. And don&#x27;t we are left with a Z. What a negative one. And these are our two solutions.

Karuna Ramroop · Answer

All right, So we have the equation three times the absolute value of explosive tube plus four is eating to 13. So with absolute value equations, the first thing I like to do is get the absolute value all by itself. So we&#x27;re gonna start by getting rid of this plus four on the left hand side of the absolute value. Did you that I&#x27;m gonna subtract four from both sides. That way, this cancels and we&#x27;re just left with the three turns, the absolute value of explosive issue. And then on the right side, we have 13 minus four, which is nine. And the next thing we&#x27;re gonna do is we&#x27;re gonna get rid of the three that&#x27;s being multiplied to the absolute value. To do that, we&#x27;re just going to you. But on that way, these cancel out and we&#x27;re just looked with the absolute value. And then onwards, I&#x27;d be of nine divided by three, which is three. So now that the absolute value was all by itself, we&#x27;re going to interpret what it&#x27;s telling us. Absolute value just means distance from zero. So, really, what this region is saying is that this quantity X plus two is three spaces away from zero. So there are two numbers that will satisfy that. Um, first, we can see that if it is expose Chu is three spaces to the right of zero than exposed to equals Positive three. Or if explosives Chu is three spaces to the left of zero, then exposed to equals Negative three. So this gives us two different equations. So we just have to solve both of these equations to figure out what X is. So in the first equation, we&#x27;re gonna so for X. By getting rid of that plus shoots, organist, subtract two from both sides so that this cancels and then we get X equals three minus two, which is one we have our first solution for the second solution. Again, we&#x27;re gonna get X alone by getting rid of that close to by subtracting two so that this cancels and then we get X equals negative three minus two, which is negative. Five. So we have our two solutions X equals one. The next equals negative five

Joshua Utley · Answer

we were asked to solve the absolute value equation for X. We need to isolate the absolute value first by subtracting two from each side, and we&#x27;re left with seven minus X. Absolute value was equal to 10. So the two equations that you get from that is seven minus X is equal to 10 and seven, minus X is equal to minus 10 and so subtract seven from both sides. Get minus X equal two months 23 and now X is equal to minus three Then and then on the other side, I can subtract seven from both sides again, minus X is equal to minus 17. X is equal 17 and now I just need to plug these answers in. Check my plug in minus three for X. Here I get seven minus minus three. So that&#x27;s 10 absolute value. Tennis. Still, 10 plus two is 12. This world works, and then if I plug in 17 I have seven minus 17 which is going to be minus 10 in the absolute value. So that&#x27;s going to become 10 plus two is 12. It&#x27;s about that These work and there&#x27;s your solutions

Problem

In $3-14,$ write the solution set of each equatio…

Problem 12 Easy Difficulty

In $3-14,$ write the solution set of each equation.
$$
|2 x-5|+2=13
$$

Answer

$x=-3,8$

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Ann Xavier Gantert

Algebra 2 and Trigonometry

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Absolute Value - Example 1

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$x=-3,8$

Algebra 2 and Trigonometry

Grace H.

Catherine R.

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Absolute Value - Example 1

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Ann Xavier GantertAlgebra 2 and Trigonometry

Grace H.

Catherine R.

Caleb E.

Michael J.

Ann Xavier Gantert

Algebra 2 and Trigonometry