Hello, Sucker Punch!
2. Does the equation 3x³ - sin(x) + 3 = 0 have a solution?
If that's the exact question, they did not ask for the solution(s).
If they want a Yes-or-No answer, the answer is: Yes.
We cannot solve for x; we can only approximate the value.
We have: .3x³ + 3 .= .sin(x)
. . and we want the intersection(s) of the curves: .y = 3x³ + 3 .and .y = sin(x).
If we sketch the two graphs, we find an intersection in Quadrant 3.