We are given the equation:

\[
\frac{y}{2x} = \frac{-456}{18x^2}
\]

We want to solve for \(x\). Here’s the step-by-step process:

1. **Simplify the right-hand side**:
   \[
   \frac{-456}{18x^2} = \frac{-456 \div 18}{x^2} = \frac{-456}{18x^2} = \frac{-38}{x^2}
   \]
   So the equation becomes:
   \[
   \frac{y}{2x} = \frac{-38}{x^2}
   \]

2. **Cross multiply** to eliminate the fractions:
   \[
   y \cdot x^2 = -38 \cdot 2x
   \]
   Simplify:
   \[
   yx^2 = -76x
   \]

3. **Divide both sides by \(x\) (assuming \(x \neq 0\))**:
   \[
   yx = -76
   \]

4. **Solve for \(x\)**:
   \[
   x = \frac{-76}{y}
   \]

Thus, the value of \(x\) is:

\[
x = \frac{-76}{y}
\]

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

Here are 5 related questions to explore:
1. What happens if \(x = 0\) in the original equation?
2. Can you solve for \(y\) if the value of \(x\) is given?
3. How do you handle cases where \(y = 0\)?
4. What is the effect of different values of \(y\) on \(x\)?
5. How would this equation change if the coefficient of \(x^2\) was different?

**Tip:** When solving equations with variables in both the numerator and denominator, cross multiplication is a powerful tool to eliminate fractions efficiently.

Learn how to solve the rational equation y/2x = -456/18x^2 step-by-step. This problem demonstrates the use of cross multiplication to solve for x, simplifying algebraic expressions, and is suitable for students in Grades 9-12.

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