in-3-14-write-the-solution-set-of-each-equation-82-b-39

Question

In $3-14,$ write the solution set of each equation.
$$
|8+2 b|-3=9
$$

Aditya Sood · Accepted Answer

right. The solution set of each equation absolute value of eight plus two b my history is it on tonight? So our first step is going to be to add three to both sides. So we get absolute value of eight plus to be easy for 12. And that&#x27;s important to see that this is actually in the same form as absolute value off A is going to be. And when you have form like this, there&#x27;s, ah, we want to break you down into two separate equations to get are two separate solutions. So the absolute value of a is going to be can be broken down into a zero to be and easy with negative B and you saw of each of these equations separately and you get your two solutions. So we&#x27;re just going to apply that same concept right over here for a problem. And so we&#x27;re going to break eight absolute value of eight plus two B is equal to 12. Uh, we&#x27;re gonna break that under two chunks. So on the left side, we got eight plus to be easy with 12 and on the right side, we have a place to be is it wouldn&#x27;t negative 12. And so now we&#x27;re just going to evaluate this as normal algebraic equation. So we want to subtract under on the left equation. We&#x27;re going to subtract eight from both sides, so we&#x27;re left with two B is equal to four and divide both sides by two until we get our one solution of bees that were too. Now, on the right equation, we&#x27;re gonna do a similar thing. We&#x27;re going to subtract it from both sides to get too busy with the negative 20. Divide both sides by two, and we get busy with the negative 10. And now we know that a solution for this equation is B is equal to and be easy with the negative time.

Aditya Sood · Answer

right. The solution set of each equation the absolute value of three X minus 12 is equal to nine. So we have a really useful equation over here. Very useful method of solving these equations and as the absolute value of A is equal to be right. So that&#x27;s what we&#x27;re given over here. Uh, this right over here is going to be our A and this is our be right over here. And so when you&#x27;re given a questions such as these, you want to split this into two separate questions, each of which will yield a different solution. So we get a sickle to be at a zygote, a negative view. And so we do a very similar thing over here. So we subdivide the certitude. Different equations. So three extra minus 12 is equal to positive. Nine and three x minus 12 people turn negative nine. Now, we just evaluate these by themselves, and we get our solutions. So without further ado, let&#x27;s get started. This first equation right over here. Wallace evaluated. So we at 12 to both sides and we get three X is equal to 21. Divide bow ties by three to get acceptable to seven on the right. Inside, we&#x27;re going to act after both sides again and divide by three to get X is equal to one, and these are our solutions.

Joshua Utley · Answer

whereas to solve the following absolute value in equation for sorry absolute value equation for X. And so the absolute value represents a distance of X plus eight from zero. Right? And so what you do when you have an absolute value problem like this is that you split it into two problems. A point where X plus eight equals six and X plus eight equals minus six. And basically what&#x27;s happening here is that this is a good way of making sure that when you&#x27;re on the number line, you&#x27;re not just accounting for this distance from zero. But you&#x27;re also accounting for this distance from zero, and so it&#x27;s solving the one on the left. If I subtract eight from both sides again, X is equal to minus two. And on the right, If I subtract a from both sides, I get X is equal to minus 14 and in absolute value equations, it&#x27;s very, very, very important that you check both of your answers. So if I plug minus two into this, I&#x27;m gonna get minus two plus A, which is six equals 26 that checks out and then over here, I&#x27;m going to have minus 14th plus eight equals six, which gives it the absolute value of negative six equal six, which also checks up. So both of our answers are good, and right now and again, the process of splitting these two and in court into two equations can introduce some a solutions that don&#x27;t work.

Aditya Sood · Answer

read the solution set of each equation. Absolute value for X minus 12 plus eight is equal to zero. So our first step is going to be Thio. Subtract eight from both sides. Get four X z quitter Negative for her. For we get the absolute value of four. X minus 12 is able to negative eight. Now, uh, this itself is actually going to be the last step because we noticed something quite unusual over here. And that is that this term, this ah, term right over here means that it&#x27;s going to have to be equal to negative eight. Right? And we know that the definition of, uh, an absolute value function is that whatever is within it in this case is going to be a whatever&#x27;s within the absolute value function is going to give that same thing just as a positive version. So if you put you know, negative 10 absolute value of negative 10 is going to be 10 and so this is actually just means that it&#x27;s going to have to be greater than zero. And so we already know just by looking at this, that four x minus 12 is going to have to be greater than zero, and that&#x27;s conflicting with this equation right over here that says the absolute value off for X minus 12 is going to be able to negative eight. It&#x27;s simply not possible, as it cannot be equally negative eight and be above zero at the same time, and therefore we won&#x27;t have to go any further because we know that it is now a solution.

Amy Jiang · Answer

Okay, so let&#x27;s start by subtracting and on both sides, we get negative seven. That&#x27;s negative number. So our solution set is

Xiaomeng Zhang · Answer

So for those one, we are multiply both sides by 24. So your heart when you for 3/8 plus b Overstreet he calls to 24 times five or work health. So about a distributive property. We have night laws eight b. He calls to 10. So now we minus ni on both sides we are How eight be close to one. So now we d right both side by those aides were how be Eco&#x27;s who won eight.

Problem

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

Problem 11 Medium Difficulty

In $3-14,$ write the solution set of each equation.
$$
|8+2 b|-3=9
$$

Answer

$b=-10,2$

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Ann Xavier Gantert

Algebra 2 and Trigonometry

Catherine R.

Anna Marie V.

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Absolute Value - Example 1

Absolute Value - Example 2

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$b=-10,2$

Algebra 2 and Trigonometry

Catherine R.

Anna Marie V.

Kayleah T.

Michael J.

Absolute Value - Example 1

Absolute Value - Example 2

Ann Xavier GantertAlgebra 2 and Trigonometry

Catherine R.

Anna Marie V.

Kayleah T.

Michael J.

Ann Xavier Gantert

Algebra 2 and Trigonometry