Solve the inequality for \( y \). \[ \frac{5}{6} y-3>4 y-\frac{7}{2} \] Simplify your answer as much as possible.

To solve the inequality \( \frac{5}{6} y - 3 > 4 y - \frac{7}{2} \), we start by simplifying it step by step. 1. Move all terms involving \( y \) to one side and constant terms to the other side: \[ \frac{5}{6} y - 4y > -\frac{7}{2} + 3 \] 2. Convert \( 4y \) to sixths to combine the \( y \) terms. Recall \( 4 = \frac{24}{6} \): \[ \frac{5}{6} y - \frac{24}{6} y > -\frac{7}{2} + 3 \] 3. Combine the \( y \) terms: \[ \left(\frac{5 - 24}{6}\right)y > -\frac{7}{2} + 3 \] \[ -\frac{19}{6}y > -\frac{7}{2} + 3 \] 4. Convert \( 3 \) to a fraction with a denominator of 2: \[ 3 = \frac{6}{2} \] Thus, \[ -\frac{7}{2} + \frac{6}{2} = -\frac{1}{2} \] 5. Now we have: \[ -\frac{19}{6}y > -\frac{1}{2} \] 6. Multiply through by \(-\frac{6}{19}\) (note that multiplying by a negative number flips the inequality): \[ y < \frac{-\frac{1}{2} \cdot -6}{19} \] \[ y < \frac{3}{19} \] Thus, the solution to the inequality is: \[ y < \frac{3}{19} \]