Problem preview

A-CED.3 Warmup M3-010-A13-V03

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

Classify why a constraint-set intersection is empty

Problem

An equation has algebraic solution \(x~=~-4\), but \(x\) represents a length requiring \(x~>~0\). Determine the contextual viable set and explain feasibility.

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The viable set is -4 because physical length may be any real number.

There are no viable solutions because all negative algebraic solutions are always invalid.

There are no viable solutions because the algebraic set -4 has empty intersection with the physical length domain x>0.

The viable set is -4 because any nonzero real length is allowed.

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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: Classify why a constraint-set intersection is empty