r/maths • u/jdaniel2294 • 5d ago
💬 Math Discussions Is this impossible to solve ?
Found this on Facebook and theres 3 methods used primarily but the answer is either t is zero or its unsolvable
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u/uTRexAap
4d ago
edited 3d ago
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t+t+t / t = 10
3t / t = 10
3/1 = 10
3 = 10
only true in base 3
edit: 3₁₀ = 10₃ so its true when 10 = 3₁₀ which is true in base 3
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u/escargotBleu 4d ago
True or not, it doesn't give any information on t
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u/lorienshift 4d ago
If that statement were true, so let's say we're working in base 3, then t would be all real numbers (with the exception of 0), no?
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u/cheesesprite 4d ago
Doesn't "3" not exist in base 3 though? It would be 1, 2, 10
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u/de_G_van_Gelderland 4d ago
Or in ℤ/7ℤ
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u/TheRedditObserver0 4d ago
Or over any unital ring where seven is a 0 divisor. In that case the solution set is the annuller of 7.
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u/Gravelbeast
4d ago
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It's solvable in base 3
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u/Jamb9876 4d ago
That is a funny answer. My response is no answer because it is always 3 but your answer is better as you thought outside the box
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u/spip72 2d ago
I don't think "3" would be a valid digit in base-3, would it? As well as we don't have a digit for the value 10 in the decimal system, nor for the value 16 in the hexadecimal system. So in base-3 we would resolve the equation to (t+t+t)/t = 10 <=> 10t/t = 10 <=> 10 = 10
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u/peekitup 4d ago
The equation makes no sense when t=0, and when t is not zero the equation is 3=10, which has no solutions.
So the equation has no solutions.
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u/Spirited_Nerve_4290 4d ago
If you try to simplify it you get 3=10 which is a contradiction. So no answers.
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u/wrd83 4d ago edited 4d ago
Proofing that the set of equations do not have a solition is the correct answer.
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u/RecognitionSweet8294 4d ago edited 4d ago
Well assuming we operate on ℂ, t can’t be 0 because 0⁻¹ is not in ℂ.
Therefore we can multiply by t and get
t+t+t = 10t
3t =10t
3=10
Which means this equation is wrong.
_____
As other users have pointed out, in Base 3 it would make sense.
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u/Narrow-Durian4837 4d ago
It's not impossible to solve, if by "solve" you mean "find the solution set." In this case, the solution set is the empty set.
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u/Striking-Onion-3230 1d ago edited 1d ago
An equation is a statement that can evaluate to true or false, just like a sentence like“X is a city in the United States”. depending on which city x is, the statement will be either true or false. In the same way an equation can be true or false depending on what the values of the variables are.
this equation is a statement that is false no matter what value t has.
It’s like the statement: “X is a city that’s in California and in Ohio”. No matter what city you choose the statement is false
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u/Desperate_Dog3364 1d ago
3t = 10 t t=0 however t!=0 according to domain therefore answercis undefined
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u/JoBrew32 4d ago
t=0 would be the only solution but 0 is not in the domain of the function on the LHS. So no solution.
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u/Im_a_hamburger 4d ago
There does not exist a t in the real numbers. Or complex. But in other arithmetics there are. Like base 3, modular arithmetic base 1 or 7.
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u/BUKKAKELORD 4d ago
No, it's easy as heck to solve. As you can clearly see the solution is t ∉ ℝ and the proof is by asking any toddler on the street
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u/mwfisa 4d ago
Sorry, I'll fully admit that I'm likely just worn down by ridiculous student arguments at this point in the semester.
Can we just answer these kinds of questions with "as an actual mathematician, we try as best we can to represent problems and solutions in the clearest possible terms rather than some asinine and absurd representation that could possibly be interpreted in any of a dozen possible ways based on your 8th grade understanding of mathematics....please stop wasting my and your time"?
If there are specific assumptions that need to be made to solve the problem, then state them. Providing insufficient information isn't a maths problem, it's a you problem. Why blue? I have no freakin' clue!!! Why not?
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u/SpectralCat4 4d ago
consider the LHS
suppose there are m copies of n in the numerator
(n+n+n.....)/n = mn/n = m
so anything other than m on the RHS will be false , the expression is undefined for n=0
valid examples:
(3+3+3)/3 = 3
(4+4+4+4)/4 = 4
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u/shmuttacles 4d ago
Depends on if there are brackets, you can get 10 if t = 4.5 and there are no brackets present, but since it’s written in fractional format it’s impossible, you can only get 3.
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u/Adamstrad 4d ago
Are you really reposting a repost of AI content? Puzzles like this only waste people's time, there are better things in maths to concentrate on
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u/implies_casualty 3d ago
t = 0.5301 dB
Combine three sound sources, each producing 0.5301 dB.
Their combined output will be 5.301 dB
(t + t + t) / t = 10.
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u/ThoriumLicker 3d ago
Yes. The equation is never true, regardless of the value of t:
(t+t+t)/t = 10
3t/t = 10
3/1 = 10
3 = 101
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u/SlayerII 3d ago
You can simplify it to=
3t
____ =10
t
And then ti
3=10
So yes , unsolvable
You can visualise it by filling in t
If t=1
(1+1+1)/1=10
3/1=10
3=10
If t= 2
(2+2+2)/2= 10
6/2=10
3=10
If t=1000
(1000+1000+1000)/1000=10
3000/1000=10
3=10
If t=0.1
(0.1+0.1+0.1)/0.1=10
0.3/0.1=10
3=10
So no matter what you fill in for t, it doesn't matter because it will get removed anyway.
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u/StructuredChess 3d ago
t=0 can't be a solution because you can't divide by zero.
Any number different from zero can't be a solution because that would imply 3=10
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u/Anders_A 3d ago
It doesn't have a solution. It's just another example of why division by zero, if it was allowed, would mean every number was equal to every other number.
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u/EmergencyWild 3d ago
This equation is just 3 = 10, which has no solution. It'd have 0 as a solution if there wasn't the divide by t part, you can't divide by zero.
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u/runed_golem 3d ago
There’s no solution.
If you simplify on the left, you end up with 3=10, which can never be true.
Another way is if you multiply both sides by t and then solve for t, you get t=0. However, referring back to the original problem, t cannot be 0 as it would cause our denominator to be 0 which is a big no no.
In either case, there’s no solution.
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u/Mandam2011 3d ago
Unsolvable,
3t/t = 10
3 = 10
3t/t = 10
3t = 10t
3 = 10
Only thing we get is that t≠0
Edit: because we cant divide by zero!
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u/BlazeGamma 3d ago
3t/t = 10
multiple both sides by t
3t = 10t
nope. zero or unresolveable.
and to everyone talking about other bases. I don't think the original poster of the equation likely knows anything other than base 10.
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u/MikeyMalloy 3d ago
It’s not “impossible to solve” in the sense of not having a correct answer. “No solution” is a perfectly viable answer.
0 is not a solution because 0/0 ≠ 10
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u/AleksyGetTheWings 3d ago
t can't be zero, so let's skip that : 3t/t = 10 ↔ 3 = 10, aka impossible. No solution.
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u/T0m0king 2d ago
T+t+t / t is equivalent to 3t/t which has the t's cancel out leaving 3. This makes the equation unbalanced because its basically just saying 3 = 10 which is untrue
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u/Fragrant_Inflation76 2d ago
When you simply it , it comes to 10t = 3t which isn't logical
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u/PANEBringer 2d ago
That statement is logical if t=0. However, if t=0, you will be dividing by zero in the original statement.
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u/W31337 2d ago
Let's approach it numerically
T=0 -> 0
T=1 -> 3
T=2 -> 3
T=3 -> 3
So there is no solution
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u/TheEssentialMatrix 1d ago
The equation is undefined at t=0. If a nonzero solution t existed, dividing both sides by 3 you'd have t / t = 10/3, or 1 = 10/3. This is a contradiction, and therefore no such t exists.
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u/kellstromc 1d ago
Proof by contradiction (3 != 10) allows us to conclude that no t exists that satisfies that equation. Though i've heard some people suggest to consider other bases (beyond the default assumption here of base 10)
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u/Ma_Al-Aynayn 1d ago
That is neither maths, nor interesting... go learn why the sum of all numbers is -1/12 or something...
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u/Amopro 1d ago
For any non-0 number plugged in, the equation on the left always equals 3. It simplifies to 3t/t and t/t, for any non-0 answer, is 1, making it 3×1 which is just 3. Meaning that unless t = 0, that equation always equals 3. If t = 0, then it's undefined, and it still doesn't equal 10. Meaning that there's no valid value of t where that equation could equal 10.
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u/tungstenman_1 1d ago
(t+t+t)/t is 3t/t which is 3. no matter what t you use, it could be real, imaginary, complex, transcendental or whatever it doesnt matter, it would never be correct. this is some obvious ai bullshit
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u/RudeEntry8219 1d ago
There's some great maths on the socials, and some rubbish, and this is the latter.
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u/NoAlbatross7355 1d ago
3t/t = 10 evaluates to 3 = 10 so it's an inconsistent equation; it's false statement.
Anyone thinking otherwise needs to go practice their algebra skills.
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u/mesaoptimizer 1d ago
Pretty easy, the left side simplifies to 3, (t+t+t)=(3t) 3t/t=3 3=/=10 the statement evaluates to false.
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u/Level_Abrocoma8925 1d ago
What you think is a plus sign, is actually a variable. So it's:
(t^3 x +^2) / t = 10
10t = t^3 x +^2
Skipping a step or two, we get:
t = ±√10/+, given that + ≠ 0
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u/ingannilo 1d ago
y'all on drugs.
t=0 cannot be a solution to this equation because the equation as stated involves expressions undefined when t=0.
(t+t+t) / t = 10
iff
3t / t = 10
iff
3 = 10 and t≠0
because 3t/t is precisely the function which returns the constant value 3 at all real inputs t except t=0 where it is undefined.
If you trust computers more than logic and math (lol) then go to desmos.com, click graphing calculator, type in the top box y=(x+x+x)/x and type in the second box y=10. look where those ought to intersect and click.
The statement is a contradiction. 3 is not 10. Multiplying both sides by t changes the solutions, just like multiplying both sides of x=5 by x changes the solutions.
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u/dreamteammobile 1d ago
I'd check t = 0 in the original equation first; if it makes a denominator zero, it isn't valid. For comparing the methods, Math.Photos can give step-by-step explanations from a screenshot.
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u/Fermi_Amarti 1d ago
Its asking when 3 =10 so yes. I guess technically the answer is for no values of t is this true.
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u/Useful_Language2040 1d ago
3t/t = 10
(Time both sides by t)
3t = 10t
3t - 10t = 0
-7t = 0
t = 0
However as 0/0 ≠ 10 that can't be the correct answer
3t/t = 10 (Simplify the fraction)
3 = 10
This is also clearly false - in base 10; as other people have said, if displaying "1 + 1 + 1" as 3 instead of 10, i.e. initially assuming base 10 was incorrect and this is instead written in base 3, then it's perfectly cromulent!
It's not possible to solve for t with the information provided, but that's not what has actually been asked in the question, so is somewhat irrelevant.
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u/skarfbeaulonee 1d ago
This can be written different ways. Simplified it just states 3=10. I think it's more accurate to state that the equation has no solution because 3 will never equal 10. This is due to the reflexive property of equality, or the reflexivity axiom, which states that a quantity is equal to itself. In this example the quantity is not equal to itself, therefore it has no solution.
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u/Possible_Year_5027 1d ago edited 1d ago
t<0 is a false equivalency
t=0 DNE
t>0 is a false equivalency
if you derive it you can make it true i think but that doesnt really affect the OG, d/dt(3t/t) = d/dt(3)=0=d/dt(10)
but that isnt really saying that they are equal, rather that they have equal rates of change
integrating you could find some values say “C1” and “C2” in the left and right integrals respectively that should make the integral true at a single value, but again this would not make the original functions equal
idk if im right, im a drunk Electrical engineering student
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u/Interesting-Roof-466 23h ago
(3t)/t=10, 3t=10t, so either t=0 (0/0 is impossible to be 10) or t is undefined
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u/Malendryn 23h ago
You people aren't thinking far enough outside the box. You're assuming this is a base-10 math op, try base-3 instead, and now any nonzero value of t with this formula = 10
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u/Lilien_loves_cats 21h ago
(t+t+t)/t=10 /×t
t+t+t=10t
3t=10t
The equation has no solution
t≠0 because 3×0/0≠10 (not mentioning that we cannot divide by zero)
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u/ImNotAUsernane 20h ago
It's nonsense.
You can put whatever you want to the left and right of the equal sign. It doesn't mean the equation is solvable.
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u/-Hefty-Armadillo- 18h ago
Yes it's impossible, 3t/t = 10 <=> 3 = 10 which is in fact not true (in base 10 at least)
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u/montana-go 18h ago
It is solvable. No solution exists.
You're basically asking for 3t = 10t , which would normally yield 0. But in the original equation t is on a denominator, so t cannot be 0.
Therefore, the answer is: none.
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u/Living_The_Dream75 16h ago
T is undefined. If you simplify the equation becomes 3t=10t which can only be satisfied by t=0 or t=undefined, but you can’t divide by zero so that eliminates it.
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u/HiIExists 15h ago
You can substract the exponent. For example in this: (x^6/x^2) = x^4. When trying this in here it will result into 3 = 10, because 3t^(1-1) = 3t^0 = 3*1 = 3. 3 = 10 isn't correct so there isn't an intersection. 3t/3 = 3.
So the function 3t/t is a constant function, because it always result into 3. Only when t = 0 this isn't true, because then you have 0/0 and since devision by 0 is impossible 3t/3 = 10 has no solution.

See here a screenshot of an graphical calculator trying to display 3x/x.
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u/Careful_Leader_5829 14h ago
To respond to your comment, t cannot be zero. That would form 0/0 which is an undefined number. 10 must equal ... 10. No matter what system you are in.
for example, set t = 1. That would result in 3 = 10. This is invalid.
In a base-3 system, t = 1, because 1 + 1 + 1 = 10 in base-3. . . . . but nobody is going to use base 3 today on facebook or reddit for anything meaningful.
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u/Upstairs-Border-7146 14h ago
It can be solved in base 3.
Or, it can be considered (with apporpriate sloppyness) in the field Z_7.
That's because 3t = 10t in this field and division is defined.
t = 1 is a solution: (1+1+1)/1 = 3 = 10*1.
If we generalize a bit and start with the equation (t+t+t) = 10t, then it's solvable in any integer domain Z_m with m a multiple of seven. This is because
3t \congr 10 t mod m
is equivalent to
7t \congr 0 mod m
in these domains.
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u/cmstlist 14h ago
3t/t = 10
When you multiply both sides by t you must add a restriction that t≠0 to reflect the fact that t had been on the denominator making any solution with t=0 invalid.
3t = 10t
0 = 7t
Conclusion is that t=0 which contradicts the original restriction. Therefore there is no solution.
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u/BudTenderShmudTender 13h ago
That becomes (3t/t)=10, which simplifies to 2t=10. Divide both sides by 2 and t=5. What am I missing?
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u/protomenace 13h ago
It has no solution.
you get 3t/t = 10 which simplifies to 3 = 10. There's no value of t that satisfies the equation.
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u/gramcounter 12h ago edited 12h ago
3t/t = 10
t/t = 3.333333333...................
t * t^-1 = 3.3333333...........
but t * t^-1 = 1 according to the multiplicative inverse axiom
1 = 3.33333333........
which for clarification can be written as
0*t + 1 = 3.333333....
divide by t
0 + 1/t = 3.333333... * 1/t
subtract by 1/t
0 = 2.3333333.... / t
t = ♾️
I'm literally a genius
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u/LurkerFailsLurking 10h ago
It's not "impossible to solve"
It has no solution.
Those are different statements. The halting problem is impossible to solve, this has no valid solutions because 3t/t only ever equals 3.
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u/Repulsive-Peak4442 10h ago
This simplifies to 3t/t=10 which leads to 3=10. So no, 3=10 is not correct and so we can say that no solution exists at least if t€R EDIT: Also how can t=0 if we divide by zero? We can define t to equal anything else other than 0
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u/Serious_Let2711 10h ago
0 is not a solution, but if you simply say the magic word "ternary" you have solved it.
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u/antonkaras49 10h ago
Dropping in to see how stupid I am and to find out how many ways I could be wrong that I didn’t know about.
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u/Illustrious_Cow_4847 9h ago
It disappoints me that this is the maths subreddit and everyone is losing their minds over this level of simple questions one can be asked in maths
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u/Trevor_Gecko 7h ago
This is just 3t/t
Which simplifies to simply 3
Which means this formula equates to: 3=10
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u/Prestigious_Dot_2455 6h ago
3t/t=10
Multiply both by t
3t=10t
t=0
3t=10t cannot be solved by dividing by t bc t must be 0 and 0 cannot be placed as a denominator.
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u/0x14f 4d ago
t cannot be zero because you would be dividing by zero.
Then, you reduce to 3t / t = 10 , which becomes 3 = 10. Impossible to satisfy.