naturalwaves:

Bro, you are still wrong, X > -2/3, x >4/3 is the correct set. This means that -2/3 < X > 4/3. If you look at this, it looks disjoint because we could then just say that X > 4/3 since it is greater than -2/3 as well. In such cases, rather than write X> -2/3 or X > 4/3 which is the same as -2/3 < X > 4/3, the proper way of writing it when such situation occurs is -2/3 < X < 0, X> 4/3.The only mistake I made was not to split it with the "0" interval. Therefore correct answer is -2/3 < X <0, X> 4/3



Quick check.: -2/3 is approximately -0.667 which is approximately -0.7. The set of values that will satisfy my answers for part 1 are all numbers that are greater than this(-0.7) but less than 0. Examples of such are; -0.5,-0.4,-0.3,-0.2,-0.1 etc. You can try as much as you want.
Note: All trials must be checked with the initially given inequation and not the quadratics you are trying it out with.

I even used online tools and inequality solvers online to crossycheck and this was what they showed.

masperano:


Dear Naturalwaves please find my response interspersed in yours.

Bro, you are still wrong, X > -2/3, x >4/3 is the correct set.

This is not a matter of right and wrong. I still do not know if you are just playing the game of right and wrong or you honestly do not understand what is involved in solving quadratic inequality (you tend to solve it as though you are solving quadratic equation ). I will pretend it is latter: this is the only way i can motivate myself to respond to you and also so that other persons in the forum can get one or two from it as i have from other responses in this forum. So let me dive right into it. I repeat your solution is wrong for the quadratic inequality (which was what caught my eye in your previous handwritten solution) and even for the question.

First you solved a quadratic inequality 9x^2-6x-8>0 and you rightly factorized it as (3x+2)(3x-4)>0 now this is where you went wrong: writing 3x+2>0 or 3x-4>0 solving for x and saying that is the solution of the aforementioned quadratic inequality. This IS INCORRECT. One has to be careful and be intuitive about it rather than solving it methodically.

masperano:
only way that quadratic can be greater than zero is if (3x+2)>0 AND (3x-4)>0 OR (3x+2)<0 AND (3x-4)<0((-) x (-) =+). If you solve with the first condition you get what you obtained which is (x>-2/3 and x>4/3) now this you can collapse to mean (x>4/3).

Now we apply the second condition which is ((3x+2)<0 AND (3x-4)<0) and we get (x<-2/3 and x<4/3) which simply means (x<-2/3). This implies that your solution set is (x<-2/3 and x>4/3)

masperano:

Now lets go to the real question.

If you look at this, it looks disjoint because we could then just say that X > 4/3 since it is greater than -2/3 as well. In such cases, rather than write X> -2/3 or X > 4/3 which is the same as -2/3 < X > 4/3, the proper way of writing it when such situation occurs is -2/3 < X < 0, X> 4/3.The only mistake I made was not to split it with the "0" interval. Therefore correct answer is [b]-2/3 < X <0, X> 4/3[/b]

This is factually inaccurate I suspect you know this but again let me pretend you do not know... x>4/3 x>-2/3, can never be written as -2/3 < X < 0, X> 4/3, please do not mislead people all in the quest to prove you are correct (respectable scientist do not). If you know me i have huge respect for scientist who admit that they are wrong when they realise they are(even Einstein admitted on occasions (on quantum mechanics and adding his cosmological constant to his fields equations in general relativity) ). Never put your ego ahead of objective truth. I am very willing to admit when i am wrong. The reason the solution of the question differ from the solution of your quadratic is because your quadratic inequality is not correct.

masperano:

Attached is the real quadratic inequality of your first inequality.

masperano:
for the scathing remarks.... I hold you to a very high standard, below which is unacceptable.

Cheers!

Your solution states that, X < -2/3 which implies X < -0.7. Let us pick a value that is less than -0.7 say -0.9 and substitute it into 1/(3x) + 1/4 < (3x)/8. By this, we will obtain -0.12 < -0.33 which is wrong because -0.12 is actually > -0.33.

Let us try -0.8 as well into the question. We will obtain,
-0.16 < - 0.3 which again is not true because -0.16 is > -0.3.
As you can see, these two simple checks alone shows that your solution is wrong and the answer can never be X< -2/3 and so I do not agree with you.

Betterstill , explain why your solution does not fit when checked with the question Thanks

I repeat, the correct solution to the inequation is -2/3<X <0, X> 4/3

naturalwaves:

There is nothing wrong with that. Inequalities can be solved as though they are real equestions and the intervals tested.

. You have lost touch with the concept.



This is not a matter of proving right and wrong. Every thing can be subjected to critisims and amendments made where necessary but in this case you have failed to make a valid objection.

The question was not to solve the quadratics but to solve the given inequation and find values that can satisfy that. Whatever answer you get should be cross checked with the main question.


Honestly, nothing is scathering about your remarks, it is an intellectual debate and all forms of disagreements are welcomed provided they can be proved. Now, Mr. masperano, let us carry out a simple test of your solution.

Your solution states that, X < -2/3 which implies X < -0.7. Let us pick a value that is less than -0.7 say -0.9 and substitute it into 1/(3x) + 1/4 < (3x)/8. By this, we will obtain -0.12 < -0.33 which is wrong because -0.12 is actually > -0.33.

Let us try -0.8 as well into the question. We will obtain,
-0.16 < - 0.3 which again is not true because -0.16 is > -0.3.
As you can see, these two simple checks alone shows that your solution is wrong and the answer can never be X< -2/3 and so I do not agree with you.

Betterstill , explain why your solution does not fit when checked with the question Thanks

I repeat, the correct solution to the inequation is -2/3<X <0, X> 4/3

masperano:



It is is either my response clearly went over your head or you are just purposely being intellectually dishonest. This will be my last response on this.... Let me make it very clear now.

1) My solution was to your quadratic inequality (9x^2-6x-8>0); your solution to that was x>-2/3, x>4/3 which is wrong, the correct solution is x<-2/3 and x>4/3. (Check the solution provided my Mathematica i attached ).

2) You used an online inequality software to get the actual solution to the original inequality but it is very obvious to me or to any one with a brain on his or her shoulders that you have no clue how they arrived at the solution, but instead to admit you do not know, you now tried to deceptively seek an equivalence of the original inequality solution to your erroneous solution by saying x>-2/3, x>4/3 is the same as -2/3<x<0 and x>4/3, claiming you have to split it by zero or whatever that means... this is at best laughable and further exposes your ignorance (when you are in a hole stop digging!).
I attached the true quadratic inequality of the original inequality when simplified which is (x(8+6x-9x^2)<0) which is clearly different from the quadratic you got. Now solving this quadratic Inequality you get -2/3<x<0,x>4/3 (The solution you claimed that is equal to yours). Very very dishonest.

Two things you got wrong: The very first simplification you got wrong... I even overlooked that ... and you still got the solution of your wrong simplification wrong( ) (which i provided the correct solution to). But because of your huge ego... you want to con people to believe that solution to the original inequality and yours are equal (This is what I find unacceptable). Take a look at your handwritten solution to that problem and tell me you still believe in what you did .

The solution to the original problem is -2/3<x<0, x>4/3

The solution to your quadratic inequality (9x^2-6x-8>0) (which you got by erroneously simplifying the original problem) is x< - 2/3 , x>4/3

The real simplification to the original inequality is (x(8+6x-9x^2)<0) in which the solution is -2/3<x<0, x>4/3.

Your solution x>-2/3 and x>4/3 is NOT equivalent to -2/3<x<0, x>4/3 as you deceptively claim.

Now i hope i am clear...

Cheers!

masperano:

This is not a matter of right and wrong. I still do not know if you are just playing the game of right and wrong or you honestly do not understand what is involved in solving quadratic inequality (you tend to solve it as though you are solving quadratic equation ). I will pretend it is latter: this is the only way i can motivate myself to respond to you and also so that other persons in the forum can get one or two from it as i have from other responses in this forum. So let me dive right into it. I repeat your solution is wrong for the quadratic inequality (which was what caught my eye in your previous handwritten solution) and even for the question

Mechanics96:
The points J,K,P and Q do not lie on the same line as the gradients of any pair differ from the other. I think you should check the coordinates again and repost.

bolaji3071:




That is the right question bro.

Mechanics96:


Well, it may be typographical error somewhere, but the question isn't right! The prove is not far fetched if you're still in doubt, I can solve questions for you on that, taken from well known textbooks.... Best wishes

Aybalance:
.Okay.Thanks 4 the help.But i wanna ask if physics questions are welcomed @naturalwaves

bolaji3071:


OK thanks, I would appreciate if you can solve something similar to that question so I can no the actual procedure.

naturalwaves:

The answer is wrong then. Not everything you see in a book is correct.

bolaji3071:
Find the ratio in which J(6,4) and K(-8,-14) divide the line segment joining P(-6,-4) and Q(10, 8.)


Please I need help with this question.


naturalwaves

masperano

naturalwaves:

I will try the ones I can lay my hands on .

afo7219:
Pls guys help me solve this calculation wit explanations.
Alhaji bello has 36months car loan of #50,000 @ 12% interest rate per annum. What is the MONTHLY loan repayment?

Aybalance:
ok boss.Is there is any connetion between capacitor and resistor,cus am confused.In a d.C circuit a 10mf capacitor is placed in series with 10ohm resistor.What is the total restance.Thanks

benji93:
CC: masperano,naturalwaves
I only need a contradiction to prove that a solution is wrong.
Let us test ur solution naturalwaves.
You insist that , the solution to the inequality 1/(3x)+1/4<(3x)/8 is x>-2/3,x>4/3, so we generalize this to the open interval(-2/3,∞)
1 satisfies the above interval, substituting it into the original equation, we have 7/12<3/8, which is false, this is where you had a problem, in your original solution(in pen), you wrote x>-2/3 or x>4/3, now this logic is inconsistent with the inequality (3x+2)(3x-4)>0, it should have been x>-2/3 and x>4/3, which implies x>4/3, the individual solutions x>-2/3,x>4/3 satisfy the equations on the left respectively and independently, but remember we only require the product of the 2 equations to be less than 0(you lost otuch of that while solving the problem), our individual solutions must be combined.
Masperano, apparently, you have a different solution, x<-2/3 or x>4/3, unfortunately your solution is wrong too,let's assume you are right, natural waves tried to test your solution, and he rightly tested it, though -2/3 is not -0.7, it is -0.66666666666666666...., but -0.9<-2/3, so naturalwaves' test number was correct.What appeals to me is a solution that work's not the mathematical formality.You were both wrong because your analysis was wrong, 1 half of your solution was right:x>4/3,but the other:x<-2/3 is wrong, you forget something, in your initial problem, the highest degree of x is 1, hence there is likely only 1 solution,but your intermediate solution, 36x^2-24x-32>0 has two distinct solutions,it isp ossible that only, one of the solutions of the intermediate step satisfies the main problem.To show this you will realize that the test number -0.9 satisfies the intermediate solution, but does not satisfy the main problem, which natural waves used in testing your solution. This might not have been the problem the poster intended, but nonetheless it is an interesting questions.Our solutions to problems usually depends on our inclination, some lay emphasis on mathematical formality others lay emphasis on solving the problem at hand.Whichever intermediate step you apply, your solution must satisfy your problem without condition.

benji93:
CC: masperano,naturalwaves
I only need a contradiction to prove that a solution is wrong.
Let us test ur solution naturalwaves.
You insist that , the solution to the inequality 1/(3x)+1/4<(3x)/8 is x>-2/3,x>4/3, so we generalize this to the open interval(-2/3,∞)
1 satisfies the above interval, substituting it into the original equation, we have 7/12<3/8, which is false, this is where you had a problem, in your original solution(in pen), you wrote x>-2/3 or x>4/3, now this logic is inconsistent with the inequality (3x+2)(3x-4)>0, it should have been x>-2/3 and x>4/3, which implies x>4/3, the individual solutions x>-2/3,x>4/3 satisfy the equations on the left respectively and independently, but remember we only require the product of the 2 equations to be less than 0(you lost otuch of that while solving the problem), our individual solutions must be combined.
Masperano, apparently, you have a different solution, x<-2/3 or x>4/3, unfortunately your solution is wrong too,let's assume you are right, natural waves tried to test your solution, and he rightly tested it, though -2/3 is not -0.7, it is -0.66666666666666666...., but -0.9<-2/3, so naturalwaves' test number was correct.What appeals to me is a solution that work's not the mathematical formality.You were both wrong because your analysis was wrong, 1 half of your solution was right:x>4/3,but the other:x<-2/3 is wrong, you forget something, in your initial problem, the highest degree of x is 1, hence there is likely only 1 solution,but your intermediate solution, 36x^2-24x-32>0 has two distinct solutions,it isp ossible that only, one of the solutions of the intermediate step satisfies the main problem.To show this you will realize that the test number -0.9 satisfies the intermediate solution, but does not satisfy the main problem, which natural waves used in testing your solution. This might not have been the problem the poster intended, but nonetheless it is an interesting questions.Our solutions to problems usually depends on our inclination, some lay emphasis on mathematical formality others lay emphasis on solving the problem at hand.Whichever intermediate step you apply, your solution must satisfy your problem without condition.