Sure! Let's solve the equation [tex]\( 7 = \sqrt[3]{k + 4} \)[/tex] step-by-step.
1. Start with the given equation:
[tex]\[
7 = \sqrt[3]{k + 4}
\][/tex]
2. To remove the cube root, cube both sides of the equation:
[tex]\[
7^3 = (\sqrt[3]{k + 4})^3
\][/tex]
3. Simplify the right side of the equation:
[tex]\[
7^3 = k + 4
\][/tex]
4. Calculate the cube of 7:
[tex]\[
7^3 = 343
\][/tex]
5. Now we have:
[tex]\[
343 = k + 4
\][/tex]
6. To solve for [tex]\( k \)[/tex], subtract 4 from both sides of the equation:
[tex]\[
343 - 4 = k
\][/tex]
7. Simplify the left side of the equation:
[tex]\[
339 = k
\][/tex]
Therefore, the value of [tex]\( k \)[/tex] is [tex]\( 339 \)[/tex].
The transformation and calculations give us:
[tex]\[
\boxed{k = 339}
\][/tex]
