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

$x=\left\{ -8,2 \right\}$
$\bf{\text{Solution Outline:}}$ To solve the given equation, $|x-7|=|2x+1| ,$ use the definition of an absolute 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} x-7=2x+1 \\\\\text{OR}\\\\ x-7=-(2x+1) .\end{array} Solving each equation results to \begin{array}{l}\require{cancel} x-7=2x+1 \\\\ x-2x=1+7 \\\\ -x=8 \\\\ x=-8 \\\\\text{OR}\\\\x-7=-(2x+1) \\\\ x-7=-2x-1 \\\\ x+2x=-1+7 \\\\ 3x=6 \\\\ x=\dfrac{6}{3} \\\\ x=2 .\end{array} Hence, $x=\left\{ -8,2 \right\} .$