Answer
$\{-3\}$
Work Step by Step
Raise each side to the power $3$.
$\left(\sqrt[3]{3t+1}\right)^3=(-2)^3$
$3t+1=-8$
Subtract $1$ from both sides then solve for $t$.
$\begin{align*}
3t+1-1&=-8-1\\
3t&=-9\\
\dfrac{3t}{3}&=\dfrac{-9}{3}\\
t&=-3
\end{align*}$
Check:
$\sqrt[3]{3(-3)+1}=-2$
$\sqrt[3]{-9+1}=-2$
$\sqrt[3]{-8}=-2$
$\sqrt[3]{(-2)^3}=-2$
$-2=-2$ True
Hence, the solution set is $\{-3\}$.
