solve the equation 3xy+4=8y-2x for x in terms of y.

We are given the equation:

\[
3xy + 4 = 8y - 2x
\]

### Steps to solve for \( x \) in terms of \( y \):

1. **Move all terms involving \( x \) to one side:**
   \[
   3xy + 2x = 8y - 4
   \]
   
2. **Factor out \( x \) on the left side:**
   \[
   x(3y + 2) = 8y - 4
   \]
   
3. **Solve for \( x \):**
   \[
   x = \frac{8y - 4}{3y + 2}
   \]

Thus, the solution for \( x \) in terms of \( y \) is:

\[
x = \frac{8y - 4}{3y + 2}
\]

Would you like more details on any step or have further questions?

### Related questions:
1. How would the solution change if the coefficients were different?
2. Can this expression for \( x \) be simplified further?
3. How can we graph the relationship between \( x \) and \( y \)?
4. What happens if \( y = -\frac{2}{3} \)?
5. How would you solve the same equation for \( y \) in terms of \( x \)?

### Tip:
When solving for a variable, always isolate the variable by factoring if possible, and ensure to move like terms to the same side of the equation.

Learn how to solve the linear equation 3xy + 4 = 8y - 2x for x in terms of y with a clear step-by-step solution. This problem involves key algebraic techniques, including factoring and isolating variables, suitable for students in Grades 8-10.

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