Problem preview

A-CED.3 Warmup M3-010-A09-V04

Represent constraints and systems, then interpret viable and non-viable solutions in modeling contexts.

Audit an algebraic candidate for equation and context viability

Problem

Candidate \(x~=~-6\) satisfies a design equation algebraically, but \(x\) represents a width with domain \(x~>~0~\text{centimeters}\). Decide whether the candidate is viable and justify the decision.

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Reject x=-6 centimeters because every negative candidate makes the original equation undefined.

Accept x=-6 centimeters because it lies in the positive width domain.

Accept x=-6 centimeters because algebraic solutions are always viable.

Reject x=-6 centimeters. It is algebraically valid, but a width must satisfy x>0, so it is not a viable physical dimension.

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Curriculum context

Course: Math III
Standard: A-CED.3
Category: Algebra
Domain: Creating Equations
Objective: Represent constraints and systems, then interpret viable and non-viable solutions in modeling contexts.
Problem type: Audit an algebraic candidate for equation and context viability