To find \( x \) in terms of \( y \) in the equation:

\[
4x - 9 = 8y - 1
\]

Follow these steps:

1. Add 9 to both sides of the equation to isolate the term with \( x \) on the left side:
   \[
   4x = 8y - 1 + 9
   \]
   Simplify the right side:
   \[
   4x = 8y + 8
   \]

2. Divide both sides of the equation by 4 to solve for \( x \):
   \[
   x = \frac{8y + 8}{4}
   \]
   Simplify further:
   \[
   x = 2y + 2
   \]

So, the solution is:
\[
x = 2y + 2
\]

Would you like more details or have any questions?

Here are some related questions:
1. How would you solve for \( y \) in terms of \( x \) instead?
2. What happens if the equation is \( 4x - 9 = 8y + 1 \)?
3. Can you verify the solution by substituting \( x = 2y + 2 \) back into the original equation?
4. How does the solution change if the coefficients of \( x \) and \( y \) are different?
5. What would the graph of this linear equation look like?

**Tip:** Always double-check your algebraic manipulations to avoid sign errors or miscalculations.

Learn how to find x in terms of y in the equation 4x - 9 = 8y - 1 step-by-step with detailed algebraic manipulation. This problem involves solving a linear equation, suitable for students in Grades 7-9.

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