## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$\bf{\text{Solution Outline:}}$ To solve the given equation, $|n-3|=|3-n| ,$ use the definition of absolute value equality. Then use the properties of equality to isolate the variable. $\bf{\text{Solution Details:}}$ Since $|x|=|y|$ implies $x=y \text{ or } x=-y,$ the equation above is equivalent to \begin{array}{l}\require{cancel} n-3=3-n \\\\\text{OR}\\\\ n-3=-(3-n) .\end{array} Solving each equation results to \begin{array}{l}\require{cancel} n-3=3-n \\\\ n+n=3+3 \\\\ 2n=6 \\\\ n=\dfrac{6}{2} \\\\ n=3 \\\\\text{OR}\\\\ n-3=-(3-n) \\\\ n-3=-3+n \\\\ 0=0 \text{ (TRUE)} .\end{array} Since the solution above ended with a TRUE statement, then the solution set is the set of all real numbers.