$$ 1=2y-\overline{\overline{}} $$$$ \frac{1}{3-x} $$

Given the equation:

\[ 1 = 2y - \frac{1}{3 - x} \]

we need to solve for $ x $. Here are the steps:

1. Start with the given equation:
   \[
   1 = 2y - \frac{1}{3 - x}
   \]

2. Isolate the fraction by subtracting $ 2y $ from both sides:
   \[
   1 - 2y = -\frac{1}{3 - x}
   \]

3. Multiply both sides by $-(3 - x)$ to eliminate the fraction:
   \[
   -(3 - x)(1 - 2y) = 1
   \]
   Simplify the left side:
   \[
   (3 - x)(2y - 1) = 1
   \]

4. Distribute $ (2y - 1) $:
   \[
   3(2y - 1) - x(2y - 1) = 1
   \]
   \[
   6y - 3 - x(2y - 1) = 1
   \]

5. Rearrange to isolate $ x(2y - 1) $:
   \[
   6y - 3 - 1 = x(2y - 1)
   \]
   \[
   6y - 4 = x(2y - 1)
   \]

6. Solve for $ x $ by dividing both sides by $ (2y - 1) $:
   \[
   x = \frac{6y - 4}{2y - 1}
   \]

Thus, the value of $ x $ in terms of $ y $ is:
\[
x = \frac{6y - 4}{2y - 1}
\]

Would you like more details or have any questions? Here are five related questions you might find interesting:

1. How do you solve equations involving complex fractions?
2. Can you explain the process of distributing terms in an equation?
3. What are some strategies for handling equations with variables in the denominator?
4. How do you check if your solution to an equation is correct?
5. What are some real-world applications of solving rational equations?

**Tip:** When dealing with fractions in equations, it can be helpful to multiply through by the denominator to eliminate the fraction and simplify the equation.

Learn how to solve the equation 1 = 2y - 1/(3 - x) step-by-step with detailed explanation and examples. This problem involves solving equations with rational expressions and is suitable for high school level students.

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