Intermediate Algebra (12th Edition)

$\left( -\infty,4 \right]$
$\bf{\text{Solution Outline:}}$ Use the concepts of inequalities to translate the given description, \begin{array}{l}\require{cancel}\text{ three times a number, minus 5, is no more than 7 ,}\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} 3x-5\le7 .\end{array} Using the properties of inequality, the inequality above is equivalent to \begin{array}{l}\require{cancel} 3x\le7+5 \\\\ 3x\le12 \\\\ x\le\dfrac{12}{3} \\\\ x\le4 .\end{array} In interval notation, the solution set is $\left( -\infty,4 \right] .$