## Intermediate Algebra (12th Edition)

$\left[ 13,\infty \right)$
$\bf{\text{Solution Outline:}}$ Use the concepts of inequalities to translate the given description, \begin{array}{l}\require{cancel}\text{ if $8$ is subtracted from a number, then the result is at least 5 ,}\end{array} into symbols. Then solve using the properties of inequality. Express the solution set in interval notation. $\bf{\text{Solution Details:}}$ In symbols, the given description translates to \begin{array}{l}\require{cancel} x-8\ge5 .\end{array} Using the properties of inequality, the inequality above is equivalent to \begin{array}{l}\require{cancel} x\ge5+8 \\\\ x\ge13 .\end{array} In interval notation, the solution set is $\left[ 13,\infty \right) .$