x/4 + 8/x = 3 This Algebra Equation is NOT so simple!
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- เผยแพร่เมื่อ 12 พ.ค. 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.
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.
X = 8 or x = 4
4 was the first number that made any sense in my mind and without having much of an understanding of algebra or the other methods used to solve this problem.
I went for 8
The key to solving is to get all of the terms under a common denominator. The result is a quadratic equation in the numerator, which is easily factored into the two solutions.
Exactly.
To solve the equation x/4 + 8/x = 3, we can first multiply both sides of the equation by 4x to eliminate the fractions.
(x/4 + 8/x) * 4x = 3 * 4x
x^2 + 32 = 12x
Next, rearrange the equation to set it equal to zero:
x^2 - 12x + 32 = 0
Now, we can factor this quadratic equation:
(x - 8)(x - 4) = 0
Setting each factor equal to zero gives us the possible solutions for x:
x - 8 = 0 or x - 4 = 0
x = 8 or x = 4
Therefore, the solutions to the equation x/4 + 8/x = 3 are x = 8 or x = 4.
Loved this… Thank You 🙏🏻
Thank you John, I appreciate your content.
Took me about 2 seconds to get 4 as an answer. But to do it on paper, we have x/4 + 8/x = 3. Multiply by 4x to get x^2 + 32 = 12x, or x^2 - 12x + 32 = 0, or (x - 8)(x - 4) = 0, so x = 8 and x = 4 are the answers. This could also be solved using the quadratic formula.
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
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.
(x/4)+(8/x)=3
therefore x not= 0
x × {(x/4)+(8/x)=3}
x^2/4+8=3x
4×{x^2/4+8=3x}
x^2+32=12x
x^2-12x+32=0
note => 2 solutions for x but not 0
the quadratic equation:
[-b +/-sqrt(b^2-4ac)]/2a
for
x^2-3x+8=0
a=1
b=-12
c=32
so
[-b +/-sqrt(b^2-4ac)]/2a
[12+/-sqrt(144-128)]/2
[12+/-sqrt(16)]/2
[12+/-4]/2
sol.1 x=4
sol.2 x=8
verify
(x/4)+(8/x)=3
sol.1 x=4
4/4 +8/4=?3
1+2=❤3✔️
sol.2 x=8
8/4+8/8=?3
2+1=❤3✔️
Gosh u r quick!
Beat me to the answer set:-D
X =4 or 8. Multiply through by 4x and you'll have a quadratic so make it equal zero and use the quadratic formula to solve
This was a good one. I labored for a long time before finally realizing that I had to get that x out of the denominator. So here comes the quadratic equation, and it was simple to solve.
Could you just have looked at it, and it is obvious that if you sub in x=4, both sides are gonna be the same?
@@marscience7819 Yeah, I kind of did a facepalm when I got the answers. Sure, one number plus another number equals 3. The first choice would be that one fraction is 1 and the other is 2. That would have been so easy. But I knew this was an algebra problem, so I tried to use algebra to solve it.
@@marscience7819and you missed the other value. there's actually two values for x.
Greetings. Yes, we can. The answers are X=4, 8. The first thing that has to be done is to get rid of the fractions by multiplying throughout by 4X to get X^2-12X+32=0. Thereafter, we will factorize the equation to get
(X-4)(X-8)=0. That is (X-4)=0, (X-8)=0 and X=4, X=8.
I am happy to inform you that your lessons have produced solid results.
6 months ago I would have given up on this one and now I can solve it using algebra.
Now I'll watch the video to see if my method was the right one but I'm confident it was. :)
Thanks!
Can't you just look at it, and it is 100% obvious that if you sub in x=4, it will work?
@@marscience7819 Yeap! But if you want to deal with tougher equations you need to learn algebra. In fact, I did not even think about plugging in the number 4 when I saw this problem.
In other words I went from thinking like you did- totally fine- to thinking algebra first.
So, I stand corrected in the sense that I would not have given up on the problem but I don't think the same way since I worked on my algebra skills which are still a work in progess BTW. ;)
Try this one and see how you are doing without algebra: x/89 + 143/x = 542
Just a hint: number 4 won't work. ;)
Thank you.
Use LCD to get the variable out of the denominators. Good Stuff.
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/× = 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.
I eliminated the denominators and went straight to the quadratic formula, all in my head and it took max 20 seconds...
Thank you for your service 🙏 ❤️ 🤍💙
I did not even think about using lcd. I just multiplied both sides by x and right there you have a quadratic equation… And, while factoring this out is nice, I am lazy and would just plug it into the formula😎
That's how I did it. The quadratic formula is burned into my brain
It is simple, if we state, that x is ot 0. In this case, we can multipl the equation withh 4x and get thhe quadratic equation.
x^2-12x+32=0
which leads to the 2 solutions:
x=6+-sqrt(4)
x=4 or x=8
We can state, thhat x is not 0, because otherwise the term 8/x is undefined.
x=8 and x=4 solves it.
Thank you Sir, for you're service too. Semper Fi! Sir I just added the 4 + 8 (adjacent diagonal numbers) = 12 / (4 lcd) = 3, x = 4 , easy peezy lemon squeezy right? Amen?
you missed an answer there's actually 2 values for x
That's so easy. You can see it has to be 4 and 8 just by looking at it!
By inspection, x=8. Took about 30 secs. On further thought, x could also be 4.
Well, I did it by taking care of the fractions first and then used the cross product to solve the problem.
At the end I came up with the right equation anyway i.e. x Squared + 32 = 12x
Then I substracted 12x from both sides, factored and came up with (x -4) (x - 8) = 0 and voilà!
But I could have done it by multiplying the whole equation by 4x as you did.
When I see fractions and an (=) sign I always think cross product. ;)
After 50+ years of taking algebra, I got this with no problem. Easy peasy.
I solved this in 10 seconds. Easy. Multiply both sides by 4x, the lowest common denominator. x^2 + 32 = 12x. x^2 - 12x + 32 = 0. (x - 4)(x - 8) = 0. x = 4 or 8
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.
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.
It all results in an equation x² - 12x + 32 = 0 so (x-4).(x-8) = 0 and x = 4 or x = 8
4 quarters equals a dollar 8 quarters equals 2 dollars together they equal 3 dollars way easier
super simple don't let the variable in the denominator scare you off. Like Sheldon Cooper, always wear a BOW TIE.
got it 4 & 8 solved by sight easy calculation had to be 2 + 1 and 1 + 2 thanks for the fun
yea it was real easy
Resolves to a quadratic x^2 - 12x + 32 = 0, I got the root numerically = 4 or 8
You should always use the quadratic equation. When I discovered the quadratic equation I was mad that math teachers wasted my time with factoring.
x = 8 or x = 4. Since this is a Quadratic equation, it should have two solutions.
I had it with the bow tie method in the begining with 96/32.
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!
X=4 ,2
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.
Come to the point than going on and on.
Everything ends up as a quadratic.
x=8 and 4 Did it in my head.
Looks like there are two solutions. x = {4,8}.
See sir this is a mathematics to be calculated by Brainly,tricky,bodamus,pedamus.i don't think so general way of solving for solution is not necessary here.thank q for understanding me.
Quadratic equation
8 and 4
Thank you. x=4,8
Since the answer was a whole number with no fraction and there are 2 even numbers in the equation , then x = even number. I tried 2 (nope) then 4(yep).
Lol! Good review. I guess -20 won't quite fly! How'd I do that anyway?Thank God I don't work for Boeing!
Thanks for sharing 🙂
"...don't remember much of anything other than getting yelled at..." 😆😂
me: USMC 1963-69
Semper Fi, Brother!
I solved it in one sec, just looking at the thumbnail as the notification of the video appeared.
Its 8. Super easy. 😊
The answer is
X = +4 & +8
4*8=32/4=8
=4, 8
3=12/4 so i need 4/4 + 8/4 wich means x=4
C=4,x=8
8
4
8 or 4
X=8 or X=4
I am so 🎉happy I got it 🎉🎉🎉🎉
The answer is a straight forward 4
That's half the answer.
x=8 is also a solution.
Please remember the slower ones who need the explanation. Not everyone can understand as quickly as other. Do have patience for that special group who are not as up with it.
X 4
x=4 or x=8
Solutions are 8 and 4
Just by looking at it I am saying x = 4 or 8
Why do we need algebra for this problem. I made the x 4 and did it in my head.
You did HALF of it in your head. Algebra provides a process to ensure you get ALL possible solutions. You can also get both solutions to this particular problem in your head, however, this is a VERY simple equation. Most are not.
I tried &got x=4&x=8
Could be 4 or 8.
X=8,or x=4
4 or 8
X=4 or 8
X=4, X=8
Four
I used the bow tie method first and arrived at the quadratic equation quickly.
X=8 and X=4
X =4, 8
Um, x= 8, or 4
X is 8 or 4.
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.
I don't really following you I mic your square root : ?
Yes ... or ...
x/4 + 8/x = 3
Beware!: x can't be equal to zero
x²/4x + 32/4x = 3
(x² + 32)/4x = 3
x² + 32 = 12x
x² - 12x + 32 = 0
Δ = 12² - 4·1·32 = 144 - 128 = 16
√Δ = ±√16 = ±4
• root #1: x = (-(-12) + 4)/2·1 = (12 + 4)/2 = 8
• root #2: x = (-(-12) - 4)/2·1 = (12 - 4)/2 = 4
-------------
| x = 8 |
-------------
| x = 4 |
-------------
🙂
I didn't bother to watch more than the first few minutes. It takes about a minute to solve it
X=8
X=4
Why not so simple? All the comments here prove the opposite.
x=4
Didnt watch, but cant agree with this not being easy.
Even if you do it properly and transform into quadratic function, this can be solved fast in memory.
x/4 + 8/x = 3 =>
x^2/4x + 32/4x = 3 =>
(x^2 + 32)/4x = 3 // *4x =>
X^2 + 32 = 12x // -12x =>
x^2 - 12x +32 = 0 =>
(x-4)(x-8) = 0 =>
x = 4 or x = 8
X=4
3.66666 recurring
٣،٢
32/3*2
Why all the bs. 4over 4 is 1. 8 over 4 is 2 1 plus 2 is 3.
This is was basic grade school math. You need to quite making it difficult
Whilst I agree that this could probably be explained in somewhat less than 20 minutes, you have only got half the answer there.
x=8 is also a solution.
X=1
X=2
You explain to much which deviate from yr target.we don't have too much time to explain the problem.Pse shorten the explanation.
Please remember there are others here who are not as knowledgeable as others. Have patience with the slower ones, ok. This is a how teaching goes.