Represent constraints with equations, inequalities, and systems; interpret viable and non-viable solutions in context.
Identify a missing context constraint
Problem
The model \(3x~+~2y~\le~30\) uses \(x\) and \(y\) to count purchased items. Add the missing domain requirement.
Big Picture
What this problem is really about
The given inequality controls total spending, but it does not automatically make every algebraic value realistic. We’ll identify what the existing constraint already handles, then use the fact that the variables count purchased objects to supply the missing domain conditions. Those conditions must rule out impossible counts without inventing any new budget or quantity limit.
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