Chapter 2 - Equations, Inequalities, and Problem Solving - 2.6 Solving Inequalities - 2.6 Exercise Set - Page 136: 94

$t\ge-20$

Using the Distributive Property and the properties of inequality, the solution to the given inequality, $ 5(t+3)+9\ge3(t-2)-10 ,$ is \begin{array}{l}\require{cancel} 5(t)+5(3)+9\ge3(t)+3(-2)-10 \\\\ 5t+15+9\ge3t-6-10 \\\\ 5t+24\ge3t-16 \\\\ 5t-3t\ge-16-24 \\\\ 2t\ge-40 \\\\ t\ge-\dfrac{40}{2} \\\\ t\ge-20 .\end{array}