Solve the Fraction Equation: -1/2(x - 1/4) = 1/2(3 - x)

Solve for X:

$-\frac{1}{2}(x-\frac{1}{4})=\frac{1}{2}(3-x)$

To solve the given equation, follow these steps:

• Step 1: Distribute the fractions
  For the left side: $-\frac{1}{2}(x-\frac{1}{4}) = -\frac{1}{2}x + \frac{1}{8}$.
  For the right side: $\frac{1}{2}(3-x) = \frac{3}{2} - \frac{1}{2}x$.
• Step 2: Set the distributed expressions equal to each other
  Equation: $-\frac{1}{2}x + \frac{1}{8} = \frac{3}{2} - \frac{1}{2}x$.
• Step 3: Simplify and solve for $x$
  Notice that the $-\frac{1}{2}x$ terms cancel each other on both sides of the equation:
  $\frac{1}{8} = \frac{3}{2}$.
  This clearly is not possible since $\frac{1}{8}$ is not equal to $\frac{3}{2}$.
• Conclusion: Determine if a solution exists
  The result indicates a contradiction because both sides of the equation cannot be equal. This implies that no value of $x$ will satisfy the equation.

Therefore, the solution to the problem is that there is no solution.