Question

which of the following correctly solves for x in the equation $2x^{\frac{1}{3}} + 6 = 18$? (1 point)\
\bigcirc $24^3$\
\bigcirc 18\
\bigcirc $12^3$\
\bigcirc 216

Explanation:

Step1: Isolate the term with \( x \)

Subtract 6 from both sides of the equation \( 2x^{\frac{1}{3}} + 6 = 18 \):
\( 2x^{\frac{1}{3}} = 18 - 6 \)
\( 2x^{\frac{1}{3}} = 12 \)

Step2: Solve for \( x^{\frac{1}{3}} \)

Divide both sides by 2:
\( x^{\frac{1}{3}} = \frac{12}{2} \)
\( x^{\frac{1}{3}} = 6 \)

Step3: Solve for \( x \)

Cube both sides to eliminate the cube root:
\( (x^{\frac{1}{3}})^3 = 6^3 \)
\( x = 216 \)

Answer:

216