## College Algebra (11th Edition)

$x=\left\{ -1,5 \right\}$
$\bf{\text{Solution Outline:}}$ To solve the given equation, $|2-x|-3=0 ,$ use the properties of equality to isolate the absolute value expression. Then use the definition of absolute value equality. $\bf{\text{Solution Details:}}$ Using the properties of equality, the equation above is equivalent to \begin{array}{l}\require{cancel} |2-x|=3 .\end{array} Since for any $c\gt0$, $|x|=c$ implies $x=c \text{ or } x=-c,$ the equation above is equivalent to \begin{array}{l}\require{cancel} 2-x=3 \\\\\text{OR}\\\\ 2-x=-3 .\end{array} Solving each equation results to \begin{array}{l}\require{cancel} 2-x=3 \\\\ -x=3-2 \\\\ -x=1 \\\\ x=-1 \\\\\text{OR}\\\\ 2-x=-3 \\\\ -x=-3-2 \\\\ -x=-5 \\\\ x=5 .\end{array} Hence, $.$ Hence, the solutions are $x=\left\{ -1,5 \right\} .$