To solve the equation [tex]\(\sqrt[3]{6x + 4} - 8 = -4\)[/tex], follow these steps:
1. Start by isolating the cube root term:
[tex]\[
\sqrt[3]{6x + 4} = -4 + 8
\][/tex]
Simplifying gives:
[tex]\[
\sqrt[3]{6x + 4} = 4
\][/tex]
2. Cube both sides to eliminate the cube root:
[tex]\[
( \sqrt[3]{6x + 4} )^3 = 4^3
\][/tex]
This simplifies to:
[tex]\[
6x + 4 = 64
\][/tex]
3. Solve for [tex]\(x\)[/tex]:
[tex]\[
6x + 4 = 64
\][/tex]
Subtract 4 from both sides:
[tex]\[
6x = 60
\][/tex]
Divide both sides by 6:
[tex]\[
x = \frac{60}{6}
\][/tex]
Simplifying gives:
[tex]\[
x = 10
\][/tex]
The solution is [tex]\( x = 10 \)[/tex].
