Represent constraints with equations, inequalities, and systems; interpret viable and non-viable solutions in context.
Recognize when inequalities are incompatible
Problem
Determine whether the system \(x~\ge~8\) and \(x~\le~5\) is feasible. If it is feasible, give a witness; if it is not, state the conflicting constraints.
Big Picture
What this problem is really about
Feasibility requires at least one value that satisfies both bounds simultaneously. We’ll interpret one inequality as a lower ray and the other as an upper ray, then compare their endpoints to see whether the rays overlap. If the required lower value lies beyond the allowed upper value, their intersection is empty and no witness can exist.
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