To find the solution to the equation [tex]\(\sqrt[3]{2x + 5} = 5\)[/tex], let's proceed step-by-step:
1. Isolate the cube root:
The given equation is [tex]\(\sqrt[3]{2x + 5} = 5\)[/tex].
2. Eliminate the cube root:
To remove the cube root, we need to cube both sides of the equation. Cubing both sides gives:
[tex]\[
(\sqrt[3]{2x + 5})^3 = 5^3
\][/tex]
3. Simplify the equation:
This simplifies to:
[tex]\[
2x + 5 = 125
\][/tex]
4. Isolate the variable term:
Next, we need to solve for [tex]\(x\)[/tex]. First, subtract 5 from both sides to isolate the term containing [tex]\(x\)[/tex]:
[tex]\[
2x = 120
\][/tex]
5. Solve for [tex]\(x\)[/tex]:
Finally, divide both sides by 2 to find the value of [tex]\(x\)[/tex]:
[tex]\[
x = 60
\][/tex]
Therefore, the solution to the equation [tex]\(\sqrt[3]{2x + 5} = 5\)[/tex] is [tex]\(x = 60\)[/tex], which corresponds to choice C.
