Select the correct answer.

What is the value of [tex]x[/tex] in the equation [tex]1,331x^3 - 216 = 0[/tex]?

A. [tex]-\frac{6}{11}[/tex]
B. [tex]\frac{11}{6}[/tex]
C. [tex]\frac{1}{6}[/tex]
D. [tex]\frac{6}{11}[/tex]



Answer :

Alright, let's solve the equation step by step:

Given the equation:

[tex]\[ 1331x^3 - 216 = 0 \][/tex]

First, we need to isolate [tex]\(x^3\)[/tex]:

[tex]\[ 1331x^3 = 216 \][/tex]

Next, divide both sides of the equation by 1331 to solve for [tex]\( x^3 \)[/tex]:

[tex]\[ x^3 = \frac{216}{1331} \][/tex]

Now, we need to solve for [tex]\(x\)[/tex] by taking the cube root of both sides.

[tex]\[ x = \sqrt[3]{\frac{216}{1331}} \][/tex]

After calculating the value, we find:

[tex]\[ x = 0.5454545454545455 \][/tex]

Recognizing this as a common fraction, we can express this decimal in a simplified fraction.

[tex]\[ 0.5454545454545455 = \frac{6}{11} \][/tex]

So, the value of [tex]\(x\)[/tex] is:

[tex]\[ \boxed{\frac{6}{11}} \][/tex]

Thus, the correct answer is:

D. [tex]\(\frac{6}{11}\)[/tex]