Answer
$d= -8$
Work Step by Step
Given \begin{equation}
\sqrt[3]{7 d-8}=-4.
\end{equation} This is a radical equation. The solution steps are shown below.
\begin{equation}
\begin{aligned}
\sqrt[3]{7 d-8}&=-4\\
\left( \sqrt[3]{7 d-8} \right)^3 & = \left(-4 \right)^3\\
7 d-8&=-64\\
d&= \frac{-64+8}{7}\\
&= -8.
\end{aligned}
\end{equation} Check. \begin{equation}
\begin{aligned}
\sqrt[3]{7 (-8)-8}&\stackrel{?}{=} 3\\
-4& =-4\quad \quad \textbf{True}
\end{aligned}
\end{equation} The solution is $d= -8 $.
