x/4 + 8/x = 3 This Algebra Equation is NOT so simple!
Vložit
- čas přidán 12. 05. 2024
- How to solve a rational equation and check for extraneous roots. Learn more math at TCMathAcademy.com/.
TabletClass Math Academy - TCMathAcademy.com/
Help with Middle and High School Math
Test Prep for High School Math, College Math, Teacher Certification Math and More!
Popular Math Courses:
Math Foundations
tabletclass-academy.teachable...
Math Skills Rebuilder Course:
tabletclass-academy.teachable...
Pre-Algebra
tabletclass-academy.teachable...
Algebra
tabletclass-academy.teachable...
Geometry
tabletclass-academy.teachable...
Algebra 2
tabletclass-academy.teachable...
Pre-Calculus
tabletclass-academy.teachable...
Math Notes: tcmathshop.com/
If you’re looking for a math course for any of the following, check out my full Course Catalog at: TCMathAcademy.com/courses/
• MIDDLE & HIGH SCHOOL MATH
• HOMESCHOOL MATH
• COLLEGE MATH
• TEST PREP MATH
• TEACHER CERTIFICATION TEST MATH
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.
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.
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.
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.
X = 8 or x = 4
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 🙏🏻
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
(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
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.
Thank you John, I appreciate your content.
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.
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. ;)
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
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.
Use LCD to get the variable out of the denominators. Good Stuff.
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. ;)
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.
Thank you.
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.
After 50+ years of taking algebra, I got this with no problem. Easy peasy.
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.
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.
By inspection, x=8. Took about 30 secs. On further thought, x could also be 4.
Thank you for your service 🙏 ❤️ 🤍💙
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
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
It all results in an equation x² - 12x + 32 = 0 so (x-4).(x-8) = 0 and x = 4 or x = 8
x=8 and x=4 solves it.
super simple don't let the variable in the denominator scare you off. Like Sheldon Cooper, always wear a BOW TIE.
4 quarters equals a dollar 8 quarters equals 2 dollars together they equal 3 dollars way easier
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.
Resolves to a quadratic x^2 - 12x + 32 = 0, I got the root numerically = 4 or 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!
You should always use the quadratic equation. When I discovered the quadratic equation I was mad that math teachers wasted my time with factoring.
Come to the point than going on and on.
x = 8 or x = 4. Since this is a Quadratic equation, it should have two solutions.
x=8 and 4 Did it in my head.
X=4 ,2
8 and 4
Thank you. x=4,8
I had it with the bow tie method in the begining with 96/32.
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.
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 🙂
Everything ends up as a quadratic.
"...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.
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).
The answer is
X = +4 & +8
C=4,x=8
4*8=32/4=8
X=8 or X=4
=4, 8
The answer is a straight forward 4
That's half the answer.
x=8 is also a solution.
X=4, X=8
I am so 🎉happy I got it 🎉🎉🎉🎉
8 or 4
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.
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 or x=8
X 4
Solutions are 8 and 4
Four
X=8 and X=4
4 or 8
X=4 or 8
8
X=8,or x=4
4
X =4, 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.
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 |
-------------
🙂
3.66666 recurring
I used the bow tie method first and arrived at the quadratic equation quickly.
X=8
X=4
Just by looking at it I am saying x = 4 or 8
x=4
X=4
Um, x= 8, or 4
Why not so simple? All the comments here prove the opposite.
X=1
X is 8 or 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=2
X=8
x=8
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.
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.
٣،٢
32/3*2
Love your videos. But you lost me on this one😊😂
It's really not that hard if you think about it
I don't really following you I mic your square root : ?
Chris, did it take you 20 minutes..john will argue that you have to show how you got the answer but that too won't take 20 minutes.
Way too involved, 20 minutes is too much. We need to teach students how to THINK, not just do rote memorized steps. I teach at the university level and I'm getting more and more students that cannot think. This is a prime example. Almost all these problems just assume integers. If I assume that, and start thinking in terms of integers, it is 100% obvious x=4 satisfies the equation. I'm literally getting freshman that do not really know that all they are doing is trying to make the left side the same value as the right side. They literally do not understand what an equal sign means. So, they think they are supposed to go through an elaborate set of manipulations, when what they should be doing is whatever it takes to figure what value of x makes the 2 sides the same. x=4 is obvious!! If it's not obvious to a person who has graduated high school, they've learned very little. They might miss the x=8 solution, but I'd rather have a bunch of students that can just look at it, and say "Oh, it's completely obvious that x=4 gets both sides to be the same" and miss the x=8 solution then to go through a formal solution where they don't really understand what they are actually doing.
I used the bowtie method and then cross multiplied. Then I solved by factoring.
Bow tie xis 4 and 8
THERE IS NOT 2 SOLUTIONS!! x is x and only has ONE solution!!
It's a quadratic. It has two solutions. That's completely normal for a quadratic.
Too much narrative. The video could be in half of the time.