in-3-14-write-the-solution-set-of-each-equation-5-a722

Question

In $3-14,$ write the solution set of each equation.
$$
|-5 a|+7=22
$$

Joshua Utley · Accepted Answer

okay. To solve this absolute value equation, we first need to isolate the absolute value. And we can do that by subtracting seven on both sides. So 22 minus seven is 15. So I have minus five day and the absolute values is equal to 15. And now I need to split that into two separate equations. So I have minus five is equal to 15 minus five is equal to minus 15 as well. So when I solve here to divide by minus five, I&#x27;m going to get a Z equals minus three and same thing here, denied by minus five. And here again, a is equal. Positive three. Now we have to check. So if I check here with my minus three minus five times minus three in the absolute value is 15 15 plus seven is 22. So this works. And then for a equals three, it&#x27;s also going to work. It&#x27;s minus five times three is minus 15. Absolute value of it makes it 15 15 plus seven is 22. So both of these solutions work. And here&#x27;s your sort of solutions

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.

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

Joshua Utley · Answer

s so we&#x27;re asked to solve this equation when we start by splitting it up into two new equations. So four wide close to is equal to 14. But also we have to consider for awhile close to is equal to minus 14. And so, for by solving both get for why, equal to 12 wise equal to three. And then here I get 41 is equal to minus 16. After subtracting to run, dividing by four on both sides and get wise equal to minus four. I can check those solutions by plugging them in for the first phone four times three plus two. They have survived. That is 14. So that&#x27;s good. And then, for the 2nd 14 times negative four is negative. 16 plus two gives me negative 14. Absolute value of negative 14 is 14. So both of these solutions work. And so this is your final answer.

Joshua Utley · Answer

all right, we&#x27;re asked to solve this and write out the solution set of bees that solve this. And so it&#x27;s an absolute value equation. So you&#x27;re going to want to split the equation into this one and this one, and then you can solve by adding tender both sides on dividing by five so you can find be with 35. So B is equal to seven after you divide by five here and then I get five. B is equal to minus 15 after adding 10 and then after dividing my time making B is equal in my history. And so when I plugged those back in, I get the absolute value. 35 minus 10 is equal to 25 which is true. And when I plug in this one, I get minus 15 minus 10. In the absolute values is equal to 25 which is also true. So my solution, said, is the set of seven on biggest three

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.

Problem

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

Problem 10 Easy Difficulty

In $3-14,$ write the solution set of each equation.
$$
|-5 a|+7=22
$$

Answer

$a=\pm 3$

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Ann Xavier Gantert

Algebra 2 and Trigonometry

Anna Marie V.

Heather Z.

Alayna H.

Caleb E.

Absolute Value - Example 1

Absolute Value - Example 2

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$a=\pm 3$

Algebra 2 and Trigonometry

Anna Marie V.

Heather Z.

Alayna H.

Caleb E.

Absolute Value - Example 1

Absolute Value - Example 2

Ann Xavier GantertAlgebra 2 and Trigonometry

Anna Marie V.

Heather Z.

Alayna H.

Caleb E.

Ann Xavier Gantert

Algebra 2 and Trigonometry