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]
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]
