## Intermediate Algebra (12th Edition)

$x=\{ -6,-1 \}$
$\bf{\text{Solution Outline:}}$ To solve the given equation, $|7+2x|=5 ,$ use the definition of absolute value equality. Use the properties of equality to isolate the variable. $\bf{\text{Solution Details:}}$ 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} 7+2x=5 \\\\\text{OR}\\\\ 7+2x=-5 .\end{array} Solving each equation results to \begin{array}{l}\require{cancel} 7+2x=5 \\\\ 2x=5-7 \\\\ 2x=-2 \\\\ x=-\dfrac{2}{2} \\\\ x=-1 \\\\\text{OR}\\\\ 7+2x=-5 \\\\ 2x=-5-7 \\\\ 2x=-12 \\\\ x=-\dfrac{12}{2} \\\\ x=-6 .\end{array} Hence, $x=\{ -6,-1 \} .$ The colored points is the graph of the solution set.