Answer
$y=-\dfrac{5}{3}$
Work Step by Step
Using the properties of equality, the given equation, $
\sqrt[3]{3y+6}+7=8
$, is equivalent to
\begin{array}{l}
\sqrt[3]{3y+6}=8-7
\\\\
\sqrt[3]{3y+6}=1
.\end{array}
Raising both sides to the $\text{
3rd
}$ power, the solution to the equation above, $
\sqrt[3]{3y+6}=1
$, is
\begin{array}{l}
3y+6=1
\\\\
3y=1-6
\\\\
3y=-5
\\\\
y=-\dfrac{5}{3}
.\end{array}
