Create and solve one-variable equations and inequalities from contexts using all studied expression types, including simple root functions.
Write and solve a contextual constraint in one variable, including the feasible domain
Problem
Use the open-box diagram for a \(20\text{-}by-30\) sheet with \(x\text{-}by\text{-}x\) corner cuts. Write the volume equation for \(1000\), state the feasible domain, and find the feasible values of \(x\).
Use the net to name all three folded dimensions before writing the volume equation. The same dimensions also impose the feasible cut-size domain, so record that domain before solving the cubic. Every cubic root is only a candidate; the geometry decides which ones describe an actual box, and substitution checks the retained values.
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