Which of the following correctly solves for x in the equation 2x^1/3+6 =18 (1 point) Responses 18 216 12^3 24^3

Answer 1

To solve the equation \(2x^{1/3} + 6 = 18\), we can follow these steps:

1. Subtract 6 from both sides: \[ 2x^{1/3} = 18 - 6 \] \[ 2x^{1/3} = 12 \]

2. Divide both sides by 2: \[ x^{1/3} = \frac{12}{2} \] \[ x^{1/3} = 6 \]

3. Cube both sides to solve for \(x\): \[ x = 6^3 \] \[ x = 216 \]

So, the correct answer is 216.