Represent constraints and systems, then interpret viable and non-viable solutions in modeling contexts.
Judge whether a candidate solution is viable under a model and its domain
Problem
Is this candidate solution viable? Candidate \(x=3\) for \(1/(x-3)=5\).
Big Picture
What this problem is really about
A candidate must belong to the original domain before it can be tested as a solution. Inspect the denominator first and substitute the candidate there; if the expression becomes undefined, no later algebra can rescue it. This domain check is essential because clearing denominators can hide the very restriction that determines viability.
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