Answer
equivalent inequalities
Work Step by Step
$\bf{\text{Solution Outline:}}$
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 $\text{
equivalent inequalities
.}$
