Chapter 7 - Section 7.6 - Radical Equations and Problem Solving - Exercise Set - Page 453: 33

$x=5$

Using the properties of equality, the given equation, $ \sqrt[3]{6x-3}-3=0 ,$ is equivalent to \begin{array}{l}\require{cancel} \sqrt[3]{6x-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} 6x-3=27 \\\\ 6x=27+3 \\\\ 6x=30 \\\\ x=\dfrac{30}{6} \\\\ x=5 .\end{array}