## Intermediate Algebra (12th Edition)

$(-11,7)$
$\bf{\text{Solution Outline:}}$ To solve the given inequality, $|x+2|\lt9 ,$ use the definition of the absolute value less than a constant. $\bf{\text{Solution Details:}}$ Since for any $c\gt0$, $|x|\lt c$ implies $-c\lt x\lt c$ or $|x|\le c$ implies $-c\le x\le c$ the inequality above is equivalent to \begin{array}{l}\require{cancel} -9\lt x+2\lt9 .\end{array} Using the properties of inequality, the inequality above is equivalent to \begin{array}{l}\require{cancel} -9-2\lt x+2-2\lt9-2 \\\\ -11\lt x\lt7 .\end{array} Hence, the solution set is the interval $(-11,7) .$