Question

In the following exercises, solve.

$\sqrt[3]{6x+4}=4$

Short answer

The solution of the given equation is $x=10$.

Step-by-step solution

Step 1. Given information.

The given equation is:

$\sqrt[3]{6x+4}=4$

Step 2. Solve the equation.

Take cube on both sides.

$\begin{array}{rcl}(\sqrt[3]{6x+4}{)}^3& =& (4{)}^3\\ 6x+4& =& 64\\ 6x& =& 64-4\\ 6x& =& 60\end{array}$

Divide both sides by 6.

$\begin{array}{rcl}\frac{6x}{6}& =& \frac{60}{6}\\ x& =& 10\end{array}$

Step 3. Conclusion.

The solution of the given equation is $x=10$.