Solve 4 Variable Equation: a,b,c & x

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Discussion Overview

The discussion revolves around solving the equation a * (x/1000) = b - x * c for the variable x. Participants explore methods to isolate x and express it in terms of the other variables, addressing the challenges faced in manipulating the equation.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant requests assistance in solving the equation, indicating a lack of expertise in mathematical problem-solving.
  • Another participant suggests adding c*x to both sides to isolate x, implying a method to rearrange the equation.
  • A subsequent reply indicates that the original poster has already reached that point and expresses difficulty with the (x/1000) term.
  • Another suggestion is made to multiply both sides by 1000 to simplify the equation further.
  • A later post provides a detailed step-by-step transformation of the equation, ultimately expressing x in terms of a, b, and c, but does not confirm if this is the only method or if it resolves the original query.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the best method to solve the equation, and the discussion includes multiple approaches and expressions for x without resolving the initial query definitively.

Contextual Notes

There may be limitations related to the assumptions about the values of a, b, and c, as well as the potential for multiple valid approaches to solving the equation that are not fully explored.

Biaqua
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For my work, I need to solve the following equation for the variable x (if possible):

a * (x/1000) = b - x * c

Can someone please help me solve it or inform me that it is simply not possible. I'm chemist myself, so solving equations is not exactly my expertise.

Thanks in advance!
 
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First, add up c*x to both sides of the equation. Then isolate x from the left side.
 
Last edited:
Thanks, but I already got to that point. The thing is that I don't know how to solve the (x/1000) part.
 
Biaqua said:
Thanks, but I already got to that point. The thing is that I don't know how to solve the (x/1000) part.

Multiply both sides by 1000.
 
Just to make it abundantly clear:

\frac{a}{1000} x = b - c x
\frac{a}{1000} x + c x = b
(\frac{a}{1000} + c) x = b
x = \frac{b}{\frac{a}{1000} + c}
x = \frac{1000 b}{a + 1000 c}
 

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