Step 1: Understand the Equation
To solve the equation \( \frac{2}{y} - \frac{1}{2} = -\frac{1}{4} \), you need to isolate \( y \).

Step 2: Eliminate Fractions
Multiply through by the least common multiple (LCM) of the denominators (which is 4 in this case) to eliminate the fractions.
- Multiply the entire equation by 4:
\( 4 \left( \frac{2}{y} \right) - 4 \left( \frac{1}{2} \right) = 4 \left( -\frac{1}{4} \right) \)
- This simplifies to:
\( \frac{8}{y} - 2 = -1 \)

Step 3: Rearrange the Equation
Now, add 2 to both sides to isolate the term with \( y \).
- \( \frac{8}{y} = -1 + 2 \)
- Simplifying gives us:
\( \frac{8}{y} = 1 \)

Step 4: Solve for \( y \)
To find \( y \), you can cross-multiply.
- Rearranging gives:
\( 8 = y \)

Step 5: Conclusion
The solution to the equation \( \frac{2}{y} - \frac{1}{2} = -\frac{1}{4} \) is:
- \( y = 8 \)
This method effectively isolates the variable and eliminates fractions, making it easier to solve the equation step by step.