Solve simple rational and radical equations and identify extraneous solutions.
Audit and interpret each algebraic candidate in context
Problem
A rate equation has algebraically valid candidates \(x~=~-5\) and \(x~=~10\). The rate must be positive and is measured in units per hour. Check the candidates and state the retained contextual solution.
Big Picture
What this problem is really about
Audit each candidate through two separate gates. First confirm algebraic validity in the original equation; then apply the model's contextual limits, such as positivity for a physical rate. Passing the equation does not make a value meaningful in the situation, so retain only candidates that pass both gates and report the surviving quantity with its units.
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