Solving Advanced Absolute Value Equations

[@headstabber6907]

How is someone this smart to know these things they don't teach in class? THANK YOU. Such a great video. never thought a 40 minute math video could pas by so fast

[@Greenemath]

Glad it was helpful!

[@shreya...007]

Omg thank you for your existence!!! Our great maths teacher was given a transfer and we now have a terrible temporary maths teacher who literally didn't do a single question on this and expects us to just know it. So thank you for saving my exam ❤️

[@Greenemath]

You are so welcome!

[@laroujensen1094]

Really Helpful! I was trying to figure out how to solve absolute value equations with two absolute value operations and a loose number and I found this gem. Thank you!

[@Greenemath]

You are very welcome, I'm glad you found the video helpful! :)

[@mannysaikuz5924]

Dude this helped so much. You deserve WAY more subscribers. Thanks for the help!

[@Greenemath]

I'm glad it helped you!

[@bayzidhasan4089]

after 2 days I finally get it.Tnxxxx

[@Greenemath]

I'm glad to hear that!

[@bisratnetsanet1418]

really really helpful.I'm feeling that you are here to show us the brightest way.May you live long! From Ethiopia

[@Greenemath]

Thanks for the nice comment.

[@user-fd1fy1bl1e]

same,from Ethiopia too

[@everettharry8789]

Omg! I was always terrified by absolute values problems this teacher made me realized that there is nothing to it. I understood the concept and I feel like I can solve any absolute value problem thrown at me. THANK YOU so much you are such a gifted teacher. I wish you could be my math teacher.

[@Greenemath]

You're very welcome!

[@vongolaprimo6804]

Thank you so much! I forgot a lot during quarantine and this not only helped me remember it also taught me more

[@Greenemath]

Glad it helped :)

[@theesunnlightt2268]

Would you please let me know why you didn't include 1/3 and 1 - the critical points- at 11:20 and you wrote (1/3, 1) instead of [1/3, 1) for the middle section and for the last one [1, infinity)?

[@Greenemath]

When one of the absolute value expressions is zero, it's a turning point, going from neg to pos or pos to neg. So when one expression is zero, the expression itself is going to be gone. Think about the scenario where x = 1, |x - 1| + |3x - 1| = 5, so we know that x - 1 will be 0, and 3x - 1 will be positive, so now we have 3x - 1 = 5, which gives us a solution of x = 2, which doesn't work since we explicitly said that x = 1. Also, you could just say does 3(1) - 1 = 5 -> 2 = 5, so the answer is no...

[@texas_guy_85]

Best video on all of KZbin.

[@Greenemath]

Doubtful, but thanks for the nice comment.

[@kennethgoldberg83]

I had never seen these approaches before. I have found that making graphs removes a lot of the mystery. they tell very quickly the number of solutions I should expect.

[@Greenemath]

You can definitely graph each part and then find the points where they intersect. You can also solve the four possible equations and then check to throw out two extraneous solutions. Lots of ways to solve that type of equation.

[@starlix1935]

Thanks for the great explanation, helped me clear a lot of confusion I had about absolute value equations

[@Greenemath]

Glad it helped!

[@IKdeoSSa_7]

What a good video. I like your step-by-step and simplistic approach.

[@Greenemath]

Glad it was helpful!

[@boidurjodas6681]

The video was tremendously helpful! Thank you very much GreeneMath!

[@Greenemath]

Glad it was helpful!

[@lakosten2604]

Ty man saved my grade keep puttin in the work

[@Greenemath]

You are welcome.

[@mynameisbakr]

23:37 so in the lower part of the table, will the order always be : Neg. Pos. Pos Neg. Neg. Pos…? I’m not trying to fully understand, (since that’s a bit beyond my paygrade) but I’m trying to memorize the process since it’s easier

[@Greenemath]

There's not really anything to memorize. Just set up the intervals and do the test.

[@PakTryOfficial]

thank you for the explanation sir, very helpful.

[@Greenemath]

Glad it was helpful!

[@mannyballon2837]

What digital board did you use for this video?

[@Greenemath]

I think you are referring to what I am writing on? That is a Wacom tablet but you can use any tablet you want as long as it has a pencil.

[@mannyballon2837]

@@Greenemath I want a digital board for PC.

[@Greenemath]

@mannyballon2837 This company makes those but they're really made for artists. It's kind of overdoing it but I really like using it. estore.wacom.com/en-us/ estore.wacom.com/en-us/wacom-cintiq-22-dtk2260k0a.html I have the older version of the one above, again you can just use a tablet at this point. That didn't exist when I started the project.

[@94547joys]

very detailed, explained well and very helpful, thank you!

[@Greenemath]

Glad it was helpful!

[@siddhigiri2573]

Hi! the video was really helpful, thanks a lot for the tutorial...I just had one doubt in the questions with double mods, if the value of x in any interval coincides with one of the bounds of it do we consider it or not? For eg. at 14:48, in case the value of x comes 1/3 itself, would we include it in our solns??

[@Greenemath]

I would give the video another watch. I spoke about this when setting up the intervals. Write out the problem and think about what happens when x = 1/3? |3 * 1/3 - 1|, is the expression going to be negative, 0, or positive?

[@MzuvelileMboxo]

May someone please share the link to the previous lessons video on this section

[@Greenemath]

kzbin.info/www/bejne/oXPYkHummsyCeZo kzbin.info/www/bejne/aZKYn5eXacShidU

[@cfdrer6578u9]

Seeing sign charts in other than rational inequalities makes me happy :)))

[@Greenemath]

Glad to hear you liked the tutorial!

[@themvlek]

Is it the same process when dealing with absolute value inequalitys? And do you have a video specific for that, let me know

[@Greenemath]

kzbin.info/www/bejne/ane6paGtnJasadU

[@milko5009]

but if have got both 2 equations correct we take the 4 equations or what?

[@Greenemath]

I have no idea what you are asking? If you clarify your question, I'm happy to answer.

[@aaryan7490]

Could you please confirm this, because I think I found an easier method of solving the questions with 2 absolute values and the extra bit but the method makes no sense. So basically I tried to just put the extra bit on one side of the equation and the 2 absolute values on one side and made one equation with positive value of the extra bit and one equation with the negative value of the extra bit, taking the absolute values as a positive value. For each question that i tried it had worked, could you please explain why

[@Greenemath]

Your method isn't going to work. That only works if you have a single absolute value expression. |ax + b| = k, then ax + b = k or ax + b = -k, what you are trying to set up does not work because you have two absolute value expressions and a loose number. You need to either set up four different possible equations and then check for extraneous solutions or use the method proposed here which develops a rule for dropping the absolute value bars and checking to see if the solution lies in the correct interval.

[@aaryan7490]

@@Greenemath Thats what I thought too, however when i tried both the 4 different equations and also my method. The method I used gave me the 2 different answers completely disregarding the ones that didn't work. I have confirmed this because I tried it with many different equations and it worked correctly every single time. I could give you an example if you would like, but the method is quite simple so you could try it too.

[@Greenemath]

@aaryan7490 If you want to post some examples, I can show you that your method does not work. You can't set the sum or difference of two absolute value expressions equal to the number and then the negative of the number to solve that type of equation. That absolutely will not work.

[@aaryan7490]

@@Greenemath never mind I have confirmed with a friend of mine, and by chance I was solving equations that could be factorized into the same coefficients of x which then in turn the positive value and the negative value of it would cancel out hence the 2 positive value giving me the correct answer. Sorry for the misunderstanding

[@Greenemath]

@aaryan7490 It's cool, best of luck with your studies!

[@themvlek]

Thank you that's was very clear and easy to me to understand.

[@Greenemath]

Glad it was helpful!

[@slowcat-j]

thank you, you are really good at explaining

[@Greenemath]

Glad it was helpful! Good luck with your studies :)

[@ananyafikru]

Hello. I was confused why you don't use closed bracket instead of parentheses. What if we get the zeros of the absolute values as a solution? (Like in the third question when you construct table) Please reply as soon as possible.

[@Greenemath]

You might find this example helpful. kzbin.info/www/bejne/aZKYn5eXacShidU You probably need to watch the course in order. I address that exact issue in a previous lesson.

[@fenfox]

22:24 why neither included? shouldn't they be included somewhere.

[@Greenemath]

That part of the problem is purely scratch work. You may include them if you want but be very careful about how you set things up. You can do this: (-infinity, -3/5) | [-3/5, 7/2) | [7/2, infinity) or (-infinity, -3/5) | (-3/5, 7/2) | (7/2, infinity) It is not going to matter at all for an equation as long as your solution is not a breakpoint. When it is, you can just check in the original problem. Here is an example of that scenario from the practice test: kzbin.info/www/bejne/eHasq4eBpLmAbrssi=rctTs0VHRJY0nIsJ&t=1516

[@fenfox]

@@Greenemath thanks for the reply. i get it now

[@Greenemath]

@fenfox I'm really glad to hear that!

[@_ethqnol_]

|x-3|+|x-2|+|x-1|+|x+1|+|x+2|+|x+3|+|x|=12. I'm using a similar strategy as in 11:20 but I'm wondering if there is a simpler way?

[@Greenemath]

That's going to take quite a while to solve by hand. Simpler way? I don't know of any, I've never seen a problem such as that given for homework. I would use a computer to solve it in real life.

[@_ethqnol_]

@@Greenemath Hello, thanks for your response! So I figured out the problem. It's a trick question kind of. There is only one solution, x=0.

[@Greenemath]

I just saw the size of that and was immediately thinking to use Symbolab or Wolfram to get the answer. I just graphed it in desmos and got x = 0 as well.

[@iil_7777]

Really helpful . Like it

[@Greenemath]

Glad it was helpful!

[@ughvocado]

Great video! Helped a lot!

[@Greenemath]

Glad it helped!

[@NYDEV0]

Thank u very much it helps me to final exam

[@Greenemath]

Glad to hear that and good luck :)

[@bleach1402]

Thank you so much, it was really helpful for me!!

[@Greenemath]

Glad it helped!

[@it.s_mark]

How to plot the values of x in a number line?

[@Greenemath]

For an equation? You just draw a horizontal number line, find your solutions and fill them in.

[@muazzamalisaqib5329]

Great work, very interesting; thanks for sharing.

[@Greenemath]

Glad you enjoyed it!

[@tshepomotau4354]

But why did the department of education remove the absolute values from the high school syllabus in South Africa? 😢😢😢

[@Greenemath]

Those problems are rarely taught anywhere. I'm not sure why they were taken out. They only teach the simple type absolute value equations.

[@isaaccheang7371]

wat if the x cancels out?

[@Greenemath]

What's the problem?

[@JoseMora-mn2kz]

A little to fast but excellent keep up the good work greetings from mexico

[@Greenemath]

Thanks! You can always slow the player down.

[@stevenphan4453]

Thank you so much I truly appreciate you

[@Greenemath]

You are so welcome

[@lynshinluuyun3771]

Very well explained

[@Greenemath]

Glad it was helpful!

[@radheya]

great help. thank you!

[@Greenemath]

You're welcome!

[@purplelotus9064]

Thanks for the explanation

[@Greenemath]

You're welcome!

[@boredism2244]

this is really good! tysm!!

[@Greenemath]

I'm glad you like it

[@justviewer5458]

9:00

[@Greenemath]

0:00

[@justviewer5458]

Easy techniques , can i also instead of using + then - , can i just square both sides if the case is like this |x-3| = |2x-3| ?

[@Greenemath]

@@justviewer5458 That's a much easier case, you don't need to follow the thought process from this video. For your scenario you just need two set ups: x - 3 = 2x - 3 x - 3 = -(2x - 3) x = 2, 0 The problems in this video are different, they deal with having a loose number, so the two absolute value expressions can't be set equal to each other.

[@SPARKONMOTIV]

Here is where l understood double or triple or more absolute value equations clear-crystal

[@Greenemath]

Glad the video was helpful!

[@teddytech7970]

what????????/ confuse method is there any way solving in case method

[@Greenemath]

Yes, but it would take longer. You would have to think about all the possibilities. If you had something like: |ax + b| + |cx + d| = e Then you would have to do: ax + b + cx + d = e -(ax + b) + cx + d = e -(ax + b) - (cx + d) = e ax + b - (cx + d) = e This will give you extraneous solutions, so you have to go back and check each solution. This type of equation is only going to have two solutions, so two will work and two will have to be thrown out. The method in the video is much quicker.

[@slowcat-j]

can you help to solve this one |х-2|+|х+4| - |х-3| = 5 ???

[@Greenemath]

Basically, you want to follow the same steps and set up intervals. The answer is going to be x = -10 or x = 2.

[@slowcat-j]

@@Greenemath thank you 🙌. I put -10 and 2 to the place of x, and I got 5. Both of them are correct. Actually in my task I was asked to find the sum of roots. So the answer will be -10+2= -8 , right?

[@Greenemath]

@@slowcat-j Yes, but they usually ask that question with quadratics and higher. There is a specific formula you can use on those guys.

[@slowcat-j]

@@Greenemath Oh, I think I wrote my question wrongly. I'm not so good at english 😅. In the task it was asked to find the sum of all answers of x. I wrote "root" , translated wrong ))

[@Greenemath]

@@slowcat-j No, your English is perfectly fine. The answer, solution, or root all mean the same thing in Math. Basically, what values can replace the variable and give you a true statement.

[@jimbo020]

Really helpful!

[@Greenemath]

Glad it was helpful!

[@coachoikawa4951]

i was waiting to get stick bugged

[@Greenemath]

No idea what that means, but thanks for watching.

[@coachoikawa4951]

@@Greenemath Hahah 😅 its a meme But the video was very helpful XD

[@Greenemath]

@@coachoikawa4951 Oh I see, well thanks for watching :)

[@Re-nq2uh]

Thanks!

[@Greenemath]

No problem!

[@ishish3850]

gr8 video

[@Greenemath]

Glad you enjoyed it

[@Ryan-sk3zq]

thanks!

[@Greenemath]

You are welcome!

[@leonardramotoroko5434]

sorry its correct sorry for misconception

[@Greenemath]

It's okay, as long as you are learning. Good luck with your studies :)

[@maximocaceres4685]

Fellow student here! Very annoying topic indeed.

[@Greenemath]

Yeah, these are very tedious problems. Unfortunately as you progress in math you find these more often. Good luck!

[@maximocaceres4685]

@@Greenemath Yes, I'm studying linear algebra right now and some matrices are just... Let's just say they are a bit crazy. Loved your video, saw the inequalities one too. Great content, and thank you.

[@Greenemath]

@maximocaceres4685 Linear algebra is a very tedious subject if done by hand. When using a computer it becomes much more manageable.

[@vigneshv3846]

lol your two looks like a derivative symbol. nice lecture though

[@Greenemath]

Yes, like every other mathematician I have terrible handwriting.

[@vigneshv3846]

@@Greenemath Then I too wish to have a terrible handwriting one day!!

[@Greenemath]

@@vigneshv3846 Just keep practicing then. Math comes over time. I have a free website GreeneMath.com that has all the videos with practice if you want to check it out. There's also KhanAcademy.org of course and CK-12.org if you like to read.

[@shray5861]

Need more subs

[@Greenemath]

It's a math channel, the subs don't really watch new videos anyway. Good luck with your studies :)

[@wusoop1658]

👌

[@Greenemath]

Thanks for watching :)

[@mr_qualityy]

Ggs

[@Greenemath]

Alright, let me know if you have a question about absolute value equations. Good luck with your studies :)

[@mr_qualityy]

Thanks

[@Greenemath]

@@mr_qualityy You are welcome! :)