College Algebra (11th Edition)

$x=-1$
$\bf{\text{Solution Outline:}}$ To solve the given equation, $\sqrt[3]{6x+2}-\sqrt[3]{4x}=0 ,$ transpose the second term and then raise both sides to the third power. Then isolate the variable. $\bf{\text{Solution Details:}}$ Using the properties of equality, the given equation is equivalent to \begin{array}{l}\require{cancel} \sqrt[3]{6x+2}=\sqrt[3]{4x} .\end{array} Raising both sides to the third power, the given equation is equivalent to \begin{array}{l}\require{cancel} 6x+2=4x .\end{array} Using the properties of equality to isolate the variable results to \begin{array}{l}\require{cancel} 6x-4x=-2 \\\\ 2x=-2 \\\\ x=-\dfrac{2}{2} \\\\ x=-1 .\end{array}