Final answer:
To solve the equation 1/6x + 2x^3 + 4 = x + 2, multiply both sides by 6 and rearrange the terms to get a cubic equation. By using the Rational Root Theorem or substituting values, we find that x = 1 is a solution of the equation.
Step-by-step explanation:
To solve the equation 1/6x + 2x^3 + 4 = x + 2, we can simplify the equation by multiplying both sides by 6 to clear the fraction:
x + 12x^3 + 24 = 6x + 12
Next, we can rearrange the terms to get all the variables on one side:
12x^3 - 5x - 12 = 0
Now, we have a cubic equation that can be factored or solved using numerical methods. By using the Rational Root Theorem or substituting values, we find that x = 1 is a solution of the equation. Therefore, the answer is A) x = 1.