Solve for \( y \). \[ -\frac{1}{3}=\frac{1}{2} y-\frac{6}{5} \] Simplify. your answer as much as possible.

To solve for \( y \) in the equation: \[ -\frac{1}{3} = \frac{1}{2}y - \frac{6}{5}, \] follow these steps: 1. **Isolate the term with \( y \):** Add \(\frac{6}{5}\) to both sides to move the constant term to the left: \[ -\frac{1}{3} + \frac{6}{5} = \frac{1}{2}y. \] 2. **Combine the fractions on the left side:** To add \(-\frac{1}{3}\) and \(\frac{6}{5}\), find a common denominator, which is 15: \[ -\frac{5}{15} + \frac{18}{15} = \frac{13}{15}. \] So, the equation becomes: \[ \frac{13}{15} = \frac{1}{2}y. \] 3. **Solve for \( y \):** Multiply both sides by 2 to isolate \( y \): \[ y = 2 \times \frac{13}{15} = \frac{26}{15}. \] 4. **Simplify the fraction (if necessary):** \(\frac{26}{15}\) is already in its simplest form since 26 and 15 have no common factors other than 1. **Final Answer:** \[ y = \frac{26}{15} \]