Interpret absolute value as distance and use it to compare quantities and errors.
Work backward from an absolute value condition
Problem
Find \(\text{all}~\text{signed}~\text{values}\) of \(x\) that make \(|x|~=~4\).
Big Picture
What this problem is really about
Read the equation as a distance condition: x must be exactly four units from zero. Distance does not specify direction, so move four units from zero on both sides of the number line and record both signed locations. Substitute each one into the absolute-value equation to verify that the full solution set is complete.
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