Question

Select the correct answer.What is the solution to this equation? x+6)1/3-5=-2

Answer 1

`(x+6)^{(1)/(3)}-5=-2`

Express the equation as:

`\begin{gathered} \sqrt[3]{x+6}-5=-2 \\ \end{gathered}`

Add 5 to both sides:

`\begin{gathered} \sqrt[3]{x+6}-5+5=-2+5 \\ \sqrt[3]{x+6}=3 \end{gathered}`

Raise both sides to the 3rd power:

`\begin{gathered} (\sqrt[3]{x+6})^3=3^3 \\ x+6=27 \end{gathered}`

Subtract 6 from both sides:

`\begin{gathered} x+6-6=27-6 \\ x=21 \end{gathered}`