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

$\bf{\text{Solution Outline:}}$ Solve the solution sets of the given statements, \begin{array}{l}\require{cancel} x-7\gt-2 \\\text{and}\\ x\gt5 .\end{array} If the solution sets are the same, then they are equivalent. Otherwise, they are not equivalent. $\bf{\text{Solution Details:}}$ Using the properties of inequality, the solution of the first inequality is \begin{array}{l}\require{cancel} x-7\gt-2 \\\\ x\gt-2+7 \\\\ x\gt5 .\end{array} Since this is the same as the second given inequality, then the given are $\text{ equivalent inequalities .}$