Consider a simple linear equation of the form: n=\frac{2x+2}{3} Let n and x repres

Dachpunkt4cr

Dachpunkt4cr

Answered question

2022-02-22

Consider a simple linear equation of the form:
n=2x+23
Let n and x represent something that comes in whole positive quantities (for example physical objects).
How can I
1.Define the equation only for n and x that are a part of natural numbers (whole numbers >0)
2.Solve the equation satisfying the above restriction (without for instace graphing it and looking for n and x that work)
Thanks!

Answer & Explanation

ayulyndji

ayulyndji

Beginner2022-02-23Added 3 answers

If you want only integer solutions, then you have a Diophantine problem. Your equation can be written 3n=2x+2, from which you deduce that n is even. From there, it's easy to find all integer solutions. You can then select the positive ones, if any.

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