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

$t\lt-\dfrac{5}{3}$
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}