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

$\bf{\text{Solution Outline:}}$ Use the properties of inequality to solve the given inequalities, \begin{array}{l}\require{cancel} -2t+3\ge11 \\\text{and}\\ -2t\ge14 .\end{array} If the solutions are the same, then the given inequalities are equivalent. $\bf{\text{Solution Details:}}$ Using the properties of inequality, the solution of the first inequality is \begin{array}{l}\require{cancel} -2t+3\ge11 \\\\ -2t\ge11-3 \\\\ -2t\ge8 \\\\ t\le\dfrac{8}{-2} \\\\ t\le-4 .\end{array} Using the properties of inequality, the solution of the second inequality is \begin{array}{l}\require{cancel} -2t\ge14 \\\\ t\le\dfrac{14}{-2} \\\\ t\le-7 .\end{array} Since the solutions of both inequalities are NOT the same, then the given inequalities are $\text{ NOT equivalent .}$