Answer :

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]