Interpret absolute value as distance and use it to compare quantities and errors.
Judge a claim about absolute distance
Problem
A student claims \(-2\) is farther from \(0\) than \(5\). Evaluate the claim using absolute value, and report whether it is valid or invalid followed by the number farther from \(0\).
Big Picture
What this problem is really about
Test the claim by measuring distance from zero, not by looking at the signs or ordinary number order. Evaluate the absolute value of each number and compare those nonnegative distances. That comparison determines whether the claim is valid and identifies which original number is actually farther from zero.
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