To solve the equation \( x^4 - 2y = 3x \) for \( y \), follow these steps:

1. **Isolate \( y \)**:
   \[
   x^4 - 2y = 3x
   \]
   Add \( -x^4 \) to both sides:
   \[
   -2y = 3x - x^4
   \]
   Divide both sides by \(-2\):
   \[
   y = \frac{x^4 - 3x}{2}
   \]

So, the solution for \( y \) in terms of \( x \) is:
\[
y = \frac{x^4 - 3x}{2}
\]

Would you like more details or have any questions about this solution?

Here are 8 related questions for further exploration:

1. How would you find the critical points of the function \( y = \frac{x^4 - 3x}{2} \)?
2. What is the derivative of \( y \) with respect to \( x \)?
3. How does the graph of \( y = \frac{x^4 - 3x}{2} \) look like?
4. What are the x-intercepts of the function \( y = \frac{x^4 - 3x}{2} \)?
5. How do you find the points of inflection for the function \( y = \frac{x^4 - 3x}{2} \)?
6. What is the second derivative of \( y = \frac{x^4 - 3x}{2} \) and what does it tell us?
7. How do you determine the concavity of \( y = \frac{x^4 - 3x}{2} \)?
8. How does the function \( y = \frac{x^4 - 3x}{2} \) behave as \( x \) approaches infinity?

**Tip:** When solving equations, always aim to isolate the variable of interest by performing inverse operations systematically.

Learn how to solve the equation x^4 - 2y = 3x for y with a detailed step-by-step solution. This problem involves algebraic equations, including quadratic and linear equations. Suitable for high school students in Grades 10-12.

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