x/4 + 8/x = 3 This Algebra Equation is NOT so simple!
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- Опубліковано 28 вер 2024
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I try and try to listen to your video but you go off on a tangent too much. Six minutes into the video and you have not begun solving yet. Would love to learn from you but you just talk and talk and talk and ...................................
He just wasted data space
My thoughts exactly. I fast-forwarded it.
X = 8
Do you not know how to drag the video forward?
@@lamper2 I do, but sometimes he will say something pertinent to me but than he goes off again. Not a problem, just won't watch any of this videos anymore. Anywho I'm retired living comfortably, but I love learning.
Keep the videos to 5 minutes maximum. I like learning but 16-18 minutes bores me so I have stopped watching/learning.
Only the ignorant are bored!
@@ellenboyerPBIHname calling is also a common denominator with ignorance…
To add fractions you need a common denominator like you were taught in 7th grade. To do this make the common denominator 4 * x. Then multiply each term by one to get (x/4 * x/x) + (8/x * 4/4) = 3 to get the equation (x^2 + 32) / 4x = 3 . Then multiply both sides by 4x to get x^2 + 32 = 12x and put equation in standard form of x^2 - 12x +32 = 0 . Then factor to (x - 4)*(x - 8) = 0 to get the answer of 4, 8. There is no need to find the lowest common denominator or to multiply the whole equation my some magic LCD of 4*x*1.
Yes, really not that hard. Dod it in my head.
Really there are several ways of approaching this problem which is all relevant.
@@philipclifton7494, Might not be hard to solve for some of us. Problems like these have more meaning to them than just the solution.
It can be hard for people around 7-12 years old. 12+ should solve it quick with use of LCD and solving ax^2+bx+c=0.... (12x=32+x^2) 😀
@@DarVV This clearly a problem for someone that has had algebra 1 in 9th grade.
You drag it out too long.
He babble too much
@@eugenewilliams8440,
he asks you and me to understand that talking is much more amusing than algebra .
Two of the people who replied to the above comment need refresher courses in English.
The answer is x=4 and/or x=8. It's simple by doing it in steps. The first step is subtract 8/x from each side of the equation, so x/4 = 3 - 8/x The next step is to multiply both sides by 4 so x = 4(3 - 8/x) or 12 - 32/x Then multiply each side by a factor of x. X^2 = 12x - 32 Then isolate the equation to one side. X^2-12x+32=0 This factors out to (x - 4)(x-8)=0 or x=4 and/or x=8
yes I did it that way mentally
@davidseed2939 I remember in school the instructor wanted students to show their work to explain how they arrived at the answer, so the solution was just as important if not moreso than the correct answer(s).
x/4 + 8/x = 3
Let t = x/4
t + 2/t = 3
t^2 -3 t + 2 = 0
(t -1)(t-2) = 0
x = 4 t
x = 4
Or
x = 8
This is the way I did it and it seems to simplify things. Noticing the 2nd term is 2/t if the first is t is a nice simplification.
This is always where I got in trouble in school. They always wanted to show the work. They wanted to see how we solved it. That takes too long. I just look at the problem and my brain figures out the answer. This happens almost instantly
I really like your video. You are very thorough and try to point out the complexities by referring to many points of solving the equations. Yes it may seem tedious but it helps me. I still have some trouble knowing when I need to look for lowest common multiplier versus lowest common denominator. I think it takes a lot of patience and determination to get good at this stuff. I am a biologist and though I've had some training in math, I was always kind of slow, but usually I could get through the courses with a good grade. Now I am retired and I find it a fun game to redirect my attention to algebra and other math, so I hope you and I will keep enjoying the challenges. Keep up the good work, and best wishes!
It's simple enough, that I don't need to create the full quadratic equation. The mean of the roots is 3 (constant term) * 4 (recibrocal of linear term) / 2 = 12/2 = 6. Obviously x = 4 and x = 8 result in 1+2 or 2+1, both are 3. Or you calculate 8 (1/x term) * 4 (see above) = 32 = x_1 * x_2. Or you take the long way with x^2 - 12 x + 32 = 0 => x = -(-12)/2 +/- sqrt(36 - 32) = 6 +/- 2.
x/4 + 8/x = 3 -> x^2/4x + 32/4x - 3 = 0 -> ((x/2+32)/4x) - 3 = 0 -> x^2-12x+32 (Quadratic equation)
Given this quadratic equation we can solve for solutions to x using the quadratic formula: (-b+-sqrt(d))/2a where d=b^2-4ac is the discriminant to the quadratic equation:
x = (-b+-sqrt(b^2-4ac))/2a = (-(-12)+-sqrt((-12)^2-4*1*32))/2*1 = (12+-sqrt(16))/2 = 6+-2
The discriminant (16) is greater than 0 so we get 2 solutions:
x1=6+2=8
x2=6-2=4
Intuitively the solution could also have been found by simply looking at the equation x/4 + 8/x = 3 and realizing that probably the solutions are 4 and 8 by substituting into x and doing a bit of simple math: 4/4+8/4=3 as well as 8/4+8/8=3. With more complex equations and/or unintuitive values of x the best method is to use formula for the discriminant and the quadratic formula.
I followed and loved you solved the algebra!!!!
I think I knew this sinds 1962: solution x =4 and x=8; by writing first part as the sum with the common denominator 4x and multiply by 4x you get the quadratic equation:ax^2+bx+c= x^2-12x+32=0; D=b^2-4ac; x=(-b±√D)/2a (D is the Discriminant)
you did it the hard way with the -b part, but yes technically that is correct. Now, if the test giver had requested foil or factoring, then no this would be wrong.
formula for roots of a quadratic equation X**2 -12X + 32 = 0 (which we get when multiplying each element with 4X) gives us 8 and 4 as 2 roots of X
No need for complicated algebra. Use cross reduction and you get 1+2=3. The X’s cancel each other out, 4 and 8 a divisible by 4 leaving you with 1 over 1 and 2 over 1.
"Use cross reduction"
That only works *multiplying* fractions. This is addition. Anyway, what is wanted IS the X and you eliminated it completely.
@@thomasmaughan4798 so, I simply solved the equation. So, you’re right I didn’t solve for X. However, cross reduction is a form of simplifying fractions to their lowest form and does work for addition and subtraction of fractions.
@@potterspride1 Well, whatever. I trust you do not build bridges.
@@thomasmaughan4798 no, I don’t build bridges. However, if I did, I wouldn’t be using algebra to build it. I would use exact numbers, and if a number wasn’t known, I would go out and measure it again myself.
@@potterspride1 "no, I don’t build bridges."
That's a relief!
For some reason I arrived at 4 and 8 but differently. I moved the 8/x to the other side resulting in x/4 = 3 - 8/x, which becomes x/4 = (3x - 8)/x. Cross-multiplying gets me x^2 = 12x - 32, which becomes the same quadratic equation you have of x^2 - 12x + 32 = 0. Factored out that leads to 4 and 8.
why applying a non-mathematical 'trick' such as cross multiplying .
you could just bring all terms to the left and over a common denominator being 4x,
and ask : when is a fraction equal to zero ?
answer: if the numerator =0 And the denominator ≠0 .
so 4x ≠ 0 => x ≠ 0 ,
And at the same time
x² - 12x + 32 = 0 .
completing the square :
x² + 2·(-6x) + (-6)² + 32 = 0 + (-6)²
(x - 6)² = 36 - 32
x - 6 = ± √4
x = 6 ± 2 .
both possibilities correspond to x ≠ 0 .
so x = 8 or x = 4 .
You're a great teacher. Keep doing what you're doing.
Guess and check is quickest in this case. I need 2 numbers that add up to 3. Hmmm 1+2=3. Looks like 4 works in that case. Algebra is not always needed, sometimes a little number sense can work.
The general case is:
(x / a) + (na / x) = (n + 1)
That can be solved by applying this formula:
x = (a / 2) [(n + 1) ± (n - 1)]
Which is:
S: { a ; na }
Multiply by 4x to eliminate denominators.
You get a quadratic; apply the quadratic formula.
Or, even better, in this case the quadratic easily factors into a product of linear factors
(x-4)(x-8).
Gleichung mit 4x Multiplizieren --> x^2 - 12x + 32 = 0 Quadratische Ergänzung ergibt --> ( x - 6 )^2 = 4
If you have any problem as simple as this, and you are stuck after the using the LCD, I suggest trial and improvement . Clearly when x = 4, we are nearly there . Then do a long division to get the other factor, x-8. Then equate both factors to be equal to zero
X=4 & 8.
Did it in my head & within a few minutes.
This one is easy by inspection. 1+2=3, 2+1=3
I multipled both sides of the equation by x to get the variable out of the denominator. Then you get a quadratic equation. I moved everything to one side of the equation so it’s equal to 0. Then I factored to get (x-8)(x-4)=0. So the solutions are 8 and 4.
The answer is x = 4, or x = 8, and is is simple - it's solvable by inspection. 4/4 = 1, 8/4 = 2, 1+2 = 3. And 8/4 = 2, 8/8 = 1, 2+1 = 3.
If you must SOLVE it, just multiply through by 4*x:
x/4 + 8/x = 3
x^2 + 32 = 12*x
x^2 - 12*x + 32 = 0
(x - 4)*(x - 8) = 0
x = 4, x = 8
Q.E.D.
It's just a quadratic - that's about as simple as it gets.
When solving equations you move terms from one side of the equals sign to the other and change the sign. Positive terms become negative, division becomes multiplication etc it is much more efficient.
So solve for X and show your work.
I was able to get the answer by getting the right hand side of the equation equal to 0, then used the quadratic equation to solve it - got 2 answers, and both worked back in the original problem.
x/4 + 8/× = 3 = ?
cruzando as duas frações, vem:
x elv 2 + 4 X 8 / 4x = 3
x elv 2 + 32 = 12x
x elv 2 - 12x + 32 = 0
que é uma equação do 2° grau
a = x elv 2 =
b = -12
c = 32
Dois números cuja soma seja - 12 e o
produto seja 32.
Ax + Sx + P =0
S = -4 + (-8 ) = - 12
P = -4 X (-8) = 32
Entoa as raizes da equação terão os sinais trocados:
r1 = 4 e r2 = 8.
Thank you for your service. I was denied the honor in 1976 due to being an Epileptic, but so grateful to those that can and do
x/4 -3 = -8/x ==> 3x/12 -36/12 = -8/x (3x-36)/12= -8/x ==> 3x**2-36x=-96 3x**2-36x+96=0 (x-8)(x-4)=0 x=4, 8 it is very easy to solve it
what software and devices do you use or your videos?
yes, 4 and 8 are easy and intuitive, but setting up a quadratic in a slightly different way gives x=6+2xsqrt(6) , and 6-2xsqrt(6) for two more solutions.
So I switched denominators did the fractions and well x over x = 1 : 8 over 4 = 2 so 1+2= 3 : x/4 or x/8 is always = to 1 because both answers will be 4/4 or 8/8
X/4 + 8/X = 3
Muktiply both sides by 4X
Gives
X² + 32 = 12X
X² - 12X + 32 = 0
(X - 8) (X - 4) = 0
X = 8 or X = 4
It all results in an equation x² - 12x + 32 = 0 so (x-4).(x-8) = 0 and x = 4 or x = 8
Cross cancel is not correct words, but divide out is.
Yes I can solve it by looking at it. It does not take long. May be 20-30 seconds I don't know exactly I did not time myself.
What you are seeing is the schtick. He is an elite mathematician and wants to give you a real math experience. The "prollem" looks simple and turns out it is rife with pitfalls. You, therefore, can't solve it and he steps in step by step and solves it. This is how you learn math. If you want to play childhood T-ball, this is not the guy. He's gonna test you and, frankly, I like that. He also designs tests for a living, so he's going to know how folks get sidetracked. That is valuable information! Love, love, love this dude!
I am not sure, what is this about? it is a 10 seconds problem. x^2 + 32 = 12x (note x/= 0). x^2 -12x +32 = 0. (x-4)*(x-8) = 0. {x=4;x=8} It is longer to write then to solve it in ind, w/o paper!
Actually this problem is very easy to solve, as follows:
X/4 + 8/X = (X^2 + 32)/4X = 3
X^2 + 32 = 12X
X^2 - 12X + 32 =0, Now factor:
(X - 8)(X - 4) = 0
X = 8, X = 4
I failed Algebra 1 twice in junior college but it took me about three seconds to solve this equation. The answer seemed obvious immediately. What's not simple about it?
Intuitively 2+1=3, 1+2=3, but I couldn’t apply my procedure to other problems hence my weakness. I need to learn procedural steps that will apply to other problems.
In 2 section seconds - 8
Y=X/4， 2/Y=8/X，Y+2/Y=3， Y^2-3Y+2=0，（Y-1）（Y-2）=0， Y=（1，2）， X=（4，8）
Ok, if you want to go into quadratic equations. But simple logic gets y 13:04 13:04 13:04 y 13:04 y 13:04 ou there in seconds: 3 is a positive integer. Therefore no fractions possible. X therefore multiples of 4. Minimum 4, maximum 8. Try both. Voilà!
HORAH Thank you very much for your brave service to our country!
Took one look to ralize straight away just a quadratic equation -multiply through by 4x to make it look normal.
I didn'y bothering spending 20 minutes to watch the video.
This problem is EXTREMELY SIMPLE!! The result MUST equal 3, and "X" must be the same number. In this case "X" = 4. So, 4/4 = 1 + 8/4 = 2 Guess what? 1 + 2 = 3 Kindergarten wasn't wasted on me.
😂😂😂
Thanks Mr. UA-cam Math man.
What i don't get is the reason "Why" you put -12x in front of +32 =0. I cant understand the problem unless that's explained.
I eyeballed this "difficult" problem and had a working value for x in 20 seconds. When the sum total is a low integer like 3, anyone can iterate the likely possibilities and solve for x without any of the complicated algebra you claim is "required." I did!
Yes it is simple. Just find a common denominator (4x) and rewrite the equation in terms of the numerators, re-arrange the terms, and complete the square. x = 8 or 4.
Resolves to a quadratic x^2 - 12x + 32 = 0, I got the root numerically = 4 or 8
Thank you
This can be solved by basic algebra, i.e. by multiplying to clear the fractions, and then solving the resulting quadratic. But just by looking at it, it's easy to see that 8 = 2*4 and 1+2 = 2+1 = 3. Either "NOT so simple!" is clickbait, or the presenter believes that schoolkid math is difficult for most people nowadays. But then I attended high school during the 1970s, I have no idea whether math even gets taught now.
From the start you can just guess it's 4 (making 1 + 2 =3) or 8 (making 2 + 1 = 3). And all that while you are talking.
How is it not so simple? It's an extremely standard exercise.
4 goes into 8 twice so we add 2+1= 3 and bottom is 1
I love these math puzzles. Good for the noggin, which is ancient.
By simply adding it will lead to quadratic equation. Then you solve the quadratic equation is that simple
This equation does not warrant 20-minute video. Noting that x is not equal to zero, reducing it to the common denominator and solving quadratic equation is a standard practice, no mysteries here. This equation is YES, so simple.
X^2-12x+32=0
On solving we get, x=4,8.
It is so simple.
Instantly thought of quadratic equation
very interesting thanks refreshing past
x=8 and x=4 solves it.
Thanks Mr. You Tube Math man
Why isn't it simple. Multiply both sides by 4x => x^2 - 12x + 32 = 0 => x = (12 +/- SQRT(144 - 128)/2 = (12+/-4)/2 = 8, 4
Look, I'm really terrible in math but was able to figure this out in a few minutes. X=4 or X=8.
x=8 solved in 3 seconds. Of cause it can technically be 4 as well, so what is the point of having a equation where you can not know x from it?
4:4 =1 8:4 =2 1+2 + 3 Both X are 4 !
Come to the point than going on and on.
Shalom to everyone
Does the teacher John have work sheets. About 100 drrills per sheets ?
Thanks.
If you wish to skip over the yakkity-yak go to 3:40.
4/4 + 8/4 = 3
8/4 + 8/4 =3
X = 4 and 8
It was to obvious, but I don't remember how to find X if the solution had been more complicated. Expect Ill find out in the rest of the video.
Wait...8/4 + 8/4 =3?
You mean 8/4 + 8/8 = 3.
🤔😉😀😃
X = 4 . It took me longer to write this out than the 5 microseconds to solve it.
Maxima quickly finds that only 2 answers exist: x=4 and x=8
x**2-12x+32=0 (x-8)(x-4)=0 x=4, 8 it is very easy to solve it
Xis 8 and 4
Two years of algebra, one year of geometry in High School 80 yrs. of living...solidly employed all those years...Not one time did I use those skills in life...As I remember Quadratic Equations were Algebra 101 classes...The Arabs must have been bored as Hell to think this up...How did this come to be on an entrance exam? I wodda been Beter off With Senior Math and Auto shop...By the way, what was your MOS in the Crotch ?
4/4 = 1 8/4 = 2 Therefore 1 + 2 = 3 X = 4
I was always bad in maths but I could solve it in less than 10 seconds just using my head
x=8 and 4 Did it in my head.
Answer # 1 is x=
8: 8/4 +8/8 = 2+1=3. Answer # 2 is ×=4: 4/4 + 8/4 = 1+2=3.😅
my TI-84+ CE cant solve this. It says zero/error.
8 and 4
X=4
Did it in my head.
I actually got there but didn't trust my answer as I couldn't remember the reasoning.
Bro why go through the song and dance?
3= x/4+8/x
X=4 1+2=3 ?
This is one of those annoying equations that have two answers.
I vaguely remember it from school - I think it’s 4 or 8, without doing the algebra, cause I can’t remember how to do it!!!😂
He got my brain cells all jacked up😒
X = 4 4/4 =1 8/4 =2 1+2 =3
"...don't remember much of anything other than getting yelled at..." 😆😂
me: USMC 1963-69
Semper Fi, Brother!
Simple
Substitute X= 8
I did that one in my head in 8 seconds.
You finish my data with your long explaination
Xsquare-12x plus 32=0 not completed
Sim[le: work into )x-4)(x-8)= 0 and the answer is obvious!
the answers are 8 and 4 for X
A good example of why algebra is to complex to be other than useless for most of humanity. The answer here is obviously 4 . Far quicker to just try inserting a number and see what happens.And if you want to find the 8 you check and try a few more.
Bro, cross multiply fractions.
x = 4?
X=4. It’s not hard at all. Only two combinations to have a sum of 3. 0 and 3 or 1 and 2.