Represent constraints and systems, then interpret viable and non-viable solutions in modeling contexts.
Find the feasible solution set of a one-variable constraint inequality
Problem
What is the feasible solution set for this advanced inequality? \((x-1)(x-4)\ge~0\)
Big Picture
What this problem is really about
The zeros of the factors are sign-change boundaries, so use them to split the number line into intervals. Test the factor signs on each interval rather than assuming the region between the zeros works. Retain every interval where the product has the required sign, and include a boundary whenever equality makes the product acceptable.
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