Solve and graph one-variable absolute-value equations and inequalities; interpret solutions in context.
Decide whether an absolute-value equation with a negative target is possible
Problem
For \(|x-4|=-3\), identify right-side sign, possible yes/no, and solution-set classification.
Big Picture
What this problem is really about
Before splitting an absolute-value equation into cases, compare its target with the possible outputs of absolute value. We’ll use the distance interpretation to establish that range, inspect the target’s sign, and decide whether any real input could produce the required output. Only a target in the allowable range justifies creating positive and negative signed cases.
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