Certainly! Let's solve the equation step-by-step.
We are given the equation:
[tex]\[
\sqrt[3]{4x - 1} - 4 = 2
\][/tex]
Step 1: Isolate the cube root term.
First, add 4 to both sides of the equation to isolate the cube root term:
[tex]\[
\sqrt[3]{4x - 1} = 2 + 4
\][/tex]
[tex]\[
\sqrt[3]{4x - 1} = 6
\][/tex]
Step 2: Remove the cube root by cubing both sides.
To eliminate the cube root, cube both sides of the equation:
[tex]\[
\left(\sqrt[3]{4x - 1}\right)^3 = 6^3
\][/tex]
[tex]\[
4x - 1 = 216
\][/tex]
Step 3: Solve for [tex]\( x \)[/tex].
Next, add 1 to both sides to solve for [tex]\( 4x \)[/tex]:
[tex]\[
4x = 217
\][/tex]
Now, divide by 4:
[tex]\[
x = \frac{217}{4}
\][/tex]
[tex]\[
x = 54.25
\][/tex]
So, the solution set is:
[tex]\[
\boxed{54.25}
\][/tex]
