Solve Equation II: $\frac{25x-2}{4}=\frac{13x+4}{3}$

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Discussion Overview

The discussion revolves around solving the equation involving the floor function: $\left\lfloor \dfrac{25x-2}{4} \right\rfloor=\dfrac{13x+4}{3}$. Participants explore the implications of the floor function in the context of the equation.

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  • Homework-related

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  • Some participants repeat the equation, indicating a focus on its solution.
  • One participant expresses appreciation for another's contribution, suggesting a collaborative atmosphere.

Areas of Agreement / Disagreement

The discussion does not present any clear agreement or disagreement on the solution, as the posts primarily consist of repetitions and expressions of encouragement rather than substantive debate or analysis.

Contextual Notes

The discussion lacks detailed mathematical exploration or resolution of the equation, and no assumptions or conditions are explicitly stated.

anemone
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Solve the equation $\left\lfloor \dfrac{25x-2}{4} \right\rfloor=\dfrac{13x+4}{3}$.
 
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anemone said:
Solve the equation $\left\lfloor \dfrac{25x-2}{4} \right\rfloor=\dfrac{13x+4}{3}$.

Subtract 1 from both sides
$\lfloor\frac{25x-6}{4}\rfloor = \frac{13x+1}{3}$
So $\frac{13x + 1}{3}$ = integer say n
So x = $\frac{3n-1}{13}$
So we get
$\lfloor\frac{25\frac{3n-1}{13}-6}{4}\rfloor = n$
Or
$\lfloor\frac{75n-103}{52}\rfloor = n$
Or 23n-103= > 0 and < 52
Or 103 <= 23n < 155
Or $\frac{103}{23} <=n < \frac{155}{23}$
So n = 5 or 6
Hence x = $\frac{14}{13}$ or $\frac{17}{13}$
 
Well done, kaliprasad! :)

But, if you don't mind me asking, I see that we could make the substitution right from the start, why would you do so only after subtracting both sides of the equation by 1?:confused:
 
anemone said:
Well done, kaliprasad! :)

But, if you don't mind me asking, I see that we could make the substitution right from the start, why would you do so only after subtracting both sides of the equation by 1?:confused:

It is not required. I did it to make the RHS simpler but it did not help :o
 
kaliprasad said:
It is not required. I did it to make the RHS simpler but it did not help :o

I see. Thanks for the reply, kali!
 

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