To solve the equation [tex]\(\sqrt[3]{2x + 5} = 5\)[/tex], we will proceed step-by-step as follows:
1. Cubing Both Sides:
To eliminate the cube root, cube both sides of the equation:
[tex]\[
(\sqrt[3]{2x + 5})^3 = 5^3
\][/tex]
This simplifies to:
[tex]\[
2x + 5 = 125
\][/tex]
2. Isolate [tex]\(2x\)[/tex]:
Subtract 5 from both sides to isolate [tex]\(2x\)[/tex]:
[tex]\[
2x + 5 - 5 = 125 - 5
\][/tex]
[tex]\[
2x = 120
\][/tex]
3. Solve for [tex]\(x\)[/tex]:
Divide both sides by 2 to solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{120}{2}
\][/tex]
[tex]\[
x = 60
\][/tex]
The correct solution to the equation [tex]\(\sqrt[3]{2x + 5} = 5\)[/tex] is [tex]\(x = 60\)[/tex].
Therefore, the correct answer is:
C. 60
