1. The problem asks to find the interval on which the function defined by the equation $$2y^3 + 3x = 3x^{10} - x$$ is continuous. 2. First, rewrite the function explicitly if possible. However, the equation is implicit in terms of $y$ and $x$. 3. Since the function involves polynomials in $x$ and $y$, and polynomials are continuous everywhere on the real line, the function defined implicitly by this polynomial equation is continuous wherever it is defined. 4. There are no denominators or roots that could cause discontinuities. 5. Therefore, the function is continuous for all real values of $x$ and $y$ that satisfy the equation. 6. In terms of $x$, the function is continuous on the entire real line $(-\infty, \infty)$. Final answer: The function is continuous on the interval $$(-\infty, \infty)$$.