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

$NOT \ equivalent$
$\bf{\text{Solution Outline:}}$ 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 $\text{ NOT equivalent .}$