Answer
$NOT \ equivalent$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the properties of inequality to solve the given inequality, $
5-2t\lt9
.$ If the solution set of this is the same as the second inequality, $
t\gt6
,$ then the inequalities are equivalent.
$\bf{\text{Solution Details:}}$
Using the properties of inequality to isolate the variable, then
\begin{array}{l}\require{cancel}
5-2t\lt9
\\\\
-2t\lt9-5
\\\\
-2t\lt4
.\end{array}
Dividing both sides by a negative number (and consequently reversing the inequality symbol), the inequality above is equivalent to
\begin{array}{l}\require{cancel}
-2t\lt4
\\\\
t\gt\dfrac{4}{-2}
\\\\
t\gt-2
.\end{array}
Since the solution set of $t\gt-2$ is not the same as the solution set of the other given inequality, $t\gt6,$ then the two inequalities are $\text{
NOT equivalent
.}$
