Answer
$t\gt-13$
Work Step by Step
$-3t-5\lt34\longrightarrow$ add 5 to each side
$-3t-5+5\lt34+5\longrightarrow$ add
$-3t\lt39\longrightarrow$ divide each side by -3; reverse the inequality
$-3t\div-3\gt39\div-3\longrightarrow$ divide
$t\gt-13$