Answer
$c=331$
Work Step by Step
The given equation is
$\Rightarrow \sqrt[3]{3c+7}=10$
Cube each side of the equation.
$\Rightarrow (\sqrt[3]{3c+7})^3=10^3$
Simplify.
$\Rightarrow 3c+7=1000$
Subtract $7$ from each side.
$\Rightarrow 3c+7-7=1000-7$
Simplify.
$\Rightarrow 3c=993$
Divide each side by $3$.
$\Rightarrow \frac{3c}{3}=\frac{993}{3}$
Simplify.
$\Rightarrow c=331$
Check $c=331$.
$\Rightarrow \sqrt[3]{3c+7}=10$
$\Rightarrow \sqrt[3]{3(331)+7}=10$
$\Rightarrow \sqrt[3]{993+7}=10$
$\Rightarrow \sqrt[3]{1000}=10$
$\Rightarrow \sqrt[3]{10^3}=10$
$\Rightarrow 10=10$
True.
Hence, the solution is $c=331$.
