Answer
$x=-12$
Work Step by Step
Using the properties of equality, the given equation, $
\sqrt[3]{2x-3}-2=-5
,$ is equivalent to
\begin{array}{l}\require{cancel}
\sqrt[3]{2x-3}=-5+2
\\\\
\sqrt[3]{2x-3}=-3
.\end{array}
Raising both sides of the equation above to the third power, then the solution/s is/are
\begin{array}{l}\require{cancel}
2x-3=-27
\\\\
2x=-27+3
\\\\
2x=-24
\\\\
x=-\dfrac{24}{2}
\\\\
x=-12
.\end{array}
