Answer
$t\lt-\dfrac{5}{3}$
Work Step by Step
Remember that when we divide or multiply an inequality by a negative, we have to flip the sign of the inequality. Using the properties of inequality, the solution to the given inequality, $
8(2t+1)\gt4(7t+7)
,$ is
\begin{array}{l}\require{cancel}
16t+8\gt28t+28
\\\\
16t-28t\gt28-8
\\\\
-12t\gt20
\\\\
t\lt\dfrac{20}{-12}
\\\\
t\lt\dfrac{\cancel{4}\cdot5}{\cancel{4}\cdot(-3)}
\\\\
t\lt\dfrac{5}{-3}
\\\\
t\lt-\dfrac{5}{3}
.\end{array}
