$\dfrac{3+x}{2022}+\dfrac{2+x}{2023}+\dfrac{1+x}{2024}+\dfrac{x}{2025}=-4$ $(S:x=-2025)$
Solving in the usual way we find the solution. I would like to know if there is a more practical way of solving this without using least common multiple.
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@AnneBauval I think it is LCM in portugese – Older Amateur Nov 22 '23 at 19:54
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Solution is -2025 not -2005. – Older Amateur Nov 22 '23 at 20:18
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@WillJagy Why replace with x=t-2025? How did you reach that conclusion? – peta arantes Nov 22 '23 at 22:15
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@AnneBauval Yes – peta arantes Nov 22 '23 at 22:16
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@OlderAmateur correct – peta arantes Nov 22 '23 at 22:16
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4Hint: Add 1 to each term on the LHS, and factor out $2025+x$. Show that the other term is non-zero, hence we require $2025+x = 0 $. – Calvin Lin Nov 22 '23 at 22:18
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2This equation has a unique solution, and there is an obvious one: the common solution of $\dfrac{3+x}{2022}=\dfrac{2+x}{2023}=\dfrac{1+x}{2024}=\dfrac{x}{2025}=-1.$ – Anne Bauval Nov 22 '23 at 22:35
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@WillJagy I don't just want to know the resolution but how to solve it. Just repeating what you say is not learning. – peta arantes Nov 22 '23 at 23:04
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@CalvinLin perfect...thanks – peta arantes Nov 22 '23 at 23:55