To solve the equation [tex]\(\sqrt[3]{x+8} = -4\)[/tex], follow these steps:
1. Isolate the cube root: The cube root is already isolated on the left side of the equation.
[tex]\[
\sqrt[3]{x+8} = -4
\][/tex]
2. Eliminate the cube root: Raise both sides of the equation to the power of 3 to get rid of the cube root.
[tex]\[
\left(\sqrt[3]{x+8}\right)^3 = (-4)^3
\][/tex]
3. Simplify both sides:
[tex]\[
x + 8 = -64
\][/tex]
4. Solve for [tex]\( x \)[/tex]: Subtract 8 from both sides to solve for [tex]\( x \)[/tex].
[tex]\[
x + 8 - 8 = -64 - 8
\][/tex]
[tex]\[
x = -72
\][/tex]
Thus, the solution to the equation [tex]\(\sqrt[3]{x+8} = -4\)[/tex] is [tex]\( x = -72 \)[/tex].
So, the correct answer is:
[tex]\[ x = -72 \][/tex]
