Create and solve one-variable equations and inequalities from contexts using all studied expression types, including simple root functions.
Write and solve a one-variable root-function inequality from a context
Problem
Write and solve an inequality for \(\sqrt{x~-~3}\) being no more than \(5\). Include the radical domain.
Big Picture
What this problem is really about
Start with the square root's domain, since any value making the radicand negative is excluded before solving begins. On that domain, both sides are nonnegative, so squaring preserves the inequality and produces an upper bound. The solution is the intersection of that bound with the original radical domain, with endpoints checked for inclusion.
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