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anonymous
 one year ago
How do you solve absolute values with negative signs? Like 4b8+1b2+2b3=2
anonymous
 one year ago
How do you solve absolute values with negative signs? Like 4b8+1b2+2b3=2

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0By the way, b2 and 2b3 are exponents

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0When treating absolute values with variables in it is helpful to factor out as many negatives to remove them as possible. Example: \[ a +2b c  = (a2b+c) = a2b+c\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yep. I get really confused whenever variables are thrown in absolute values, since I've seen them solved so many different ways...

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0The reason this works is because if the argument of the absolute value (the quantity between the bars) is negative then the absolute value returns the NEGATIVE of that: \[5=(5) \ \ \ \ whereas \ \ \ \ 3=3\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Um... oh, yeah! That does kind of make sense! I'm kind of confused on what you showed me before this reply though...

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So looking at the reposting of the problem (thank you @zepdrix, didnt realize those were powers at first)... You will have two cases to treat

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Assuming that b is a real number... its square will always be positive so factor out the negative like I showed in my generic example and get rid of it.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0That term you can then drop the absolute value bars since it will be strictly positive

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh well I didn't want to jump right at the answer I wanted to show you an example of some generic statement with absolute value bars and show the process of factoring out a negative

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Then my second post was to show you why I could simply eliminate it after it was factored

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Can we actually start with this equation? I still have trouble understanding stuff like this, and what you're going into is really giving me a headache: 998x=2x+3

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Hahaha well thats good... think about it like lifting weights... If you lifted a feather would your arm muscles burn during the motion? Would they ache the next day?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Only with harder problems do you build your mental muscles to get stronger :D... sure no problem lets start there

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yeah, I know... I really need to wrap my mind around the simple stuff first though! I get confused so easily! D:

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Its ok dont worry about it we all have to go through it at some point :D:D

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ok so we have: \[998x = 2x+3\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0And you divide 9 to both sides right? I got a fraction, so I wasn't sure of myself there either.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0This type of problem will have two cases: First case: When (98x) < 0 Second Case: When (98x) > 0 Think you can guess why we will need to have two cases?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yes eventually but lets deal with the hard bit first.... then after that it should be easy yes?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Okay... you need two cases to show both possible solutions to the absolute value right?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Exactley... AND we can exploit the two properties I initially posted to completely remove the absolute value bars from the problem.... once we have split it up into two separate equations subject to those conditions... make sense?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0And eventually you'll need to check for extraneous solutions too right?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Are you talking about when 98x=0

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Because that wont satisfy the problem at a glance

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Well lets first handle the problem then you can refresh my memory about extraneous solutions... its seems to be blank spot for me right now

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Sorry I didn't see you send out that reply. But yeah, I never thought the absolute value signs could be changed into parentheses... The question asks me to check for extraneous solutions, which is when one of the solutions turns out to not satisfy the solution.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0AHHHH yes great point

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Once you set up the two equations you solve for them... BUT you should ALWAYS check to make sure your solutions satisfy the original system (equation)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yep! So first of all, we're supposed to divide 9 to both sides like this right? (9÷9)98x=2x+(3÷9)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yes you can start there

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0And I did it right? It's correct to get a fraction, right?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So we have \[998x = 2x+3 \\ \rightarrow \ \ \98x = \frac{2}{9}x+\frac{1}{3} \]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ignore the double bar (typo)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So we have \[998x = 2x+3 \\ \rightarrow \ \ \ 98x = \frac{2}{9}x+\frac{1}{3} \]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0What?? You can divide 9 into 2x too? Man, I never thought you could do that...

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Okay, so once it becomes 98x=2/9x+1/3 please show me how you set up the 2 possible solutions. I always get confused

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh yea sure whenever you divide (or multiply) a number to a whole side it DISTRIBUTES to sums. For any real numbers (or variables that take on real numbers (x)): \[ a(b+c)=ab+ac \ \ \ or \ \ \ \ a(x+b)=ax+ab\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So just let a be 1/9 and your'e golden :D

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ok I will do an example problem and then I want you to try your'e problem:

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I just always get confused when there's a negative number within the absolute value. Please help me figure out what to do when those show up...

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0For: \[ 2x12\] If \[ 2x12<0\] Then \[(2x12)>0\] ALWAYS Please take a second to consider this

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0If \[(2x12)\] is always positive then the absolute value bars just return the quantity. I.e. if: \[a>0 \ \ \ \ \rightarrow \ \ \ \ a=a\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So: \[(2x12)=(2x12)\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Now I have given you the seeds to actually solve both parts... so please do that and post them here when you are done :D

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So which side of the equation would you normally do that to? I thought you were supposed to do it to the right side, right?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Forget sides... we are just talking about the absolute valued term... the goal here is to figure out what to "substitute" in for the absolute value bars (in each specific case) so they are no longer in the original problem

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Think about it as breaking the problem up into the original and a new sub problem.... once we figure out the sub problem (for both cases in the original problem) we will know what will take the place of the absolute value term

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Does this make sense?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Alright... I'm still a little confused, but I'll try and solve it now

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Bingo... thats the spirit... sometimes it just takes the courage to plow ahead and see what happens :D

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Whats the worst that can happen... you get it wrong? Well at least now you will definitely know one thing that DOESNT work :D be optimistic :D:D

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Alright, so when you first start off with 98x=2/9x+1/3 98x becomes (98x)? On both sides?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0No only substitute in for the absolute value term... btw if you dont know how to use the equations tab could you please enclose your fractions in () like (2/9) for ease of reading

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Alright, I will. Sooo... only do (98x) on the positive side?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0OK whew.... If I randomly stop talking its because open study has locked up on me AGAIN today

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Hopefully this doesnt happen but be warned open study has not cooperated with me today

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I'm so sorry for my confusion. Math is definitely not my easiest class...

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh yes sorry... try and be precise with you language... sooo you are going to substitute in (98x) in for the 98x for the case when 98x<0

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Gotta work it then... Just like muscles... If you dont work them they will never grow and stay weak

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Alright, I'll do that!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So once I do that, I got: 9+8x=(2/9)x+(1/3) or 9+8x= ((2/9)x+(1/3)) Correct or incorrect?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Sorry I forgot to type it with parentheses: 98x=(2/9)x+(1/3)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Which case though be specific as to what you are trying to say... remember the two cases? Which case belongs with which substitution

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I hate to be pedantic, but this is a very important distinction because your answer may or may not be right depending on which case you assign them to... keep that in mind

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I don't know honestly. What do you mean by that?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I'm ready to give up at this point... this is getting too complicated! :(

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Sorry I got hung up for a second

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ok watch how I state 1 of the cases... and note the goal of math isnt just to get the answer, but to express that answer and your work in a way that someone reading it can know what you are doing

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0When 98x<0 ==> (98x)>0 Thus 98x=(98x)=98x Then you sub into your problem and solve for x below

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0That symbol btw ==> is just my way of doing an arrow... you read it as "implies"

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0But when you have (98x) aren't you supposed to distribute the negative sign to both numbers, thus making it 9+8x?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0AHHHH Im soooo sorry I made a typoe please hold

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0When 98x<0 ==> (98x)>0 Thus 98x=(98x)=(98x)=8x9 Then you sub into your problem and solve for x below

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I still don't understand why it doesn't become positive... thank you so much for your help, but I think I'm just goint to try and get help from my teacher.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0It is positive what do you mean?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I said 98x< SOOO [(98x)]>0... Its the whole quantity in the square brakets that are positive here so the whole quantity is unaffected by the absolute value signs since it is positive

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0If you prefer distribute the minus sign first then you will have it correct... btw you did that when you noticed my error only you didnt distribute correctly... check my corrected post a couple above
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