Solve the following in equality e) \( \frac{3 y+2}{2}-\frac{y-6}{3}>0 \)

Solve the equation \( \frac{3y+2}{2}-\frac{y-6}{3}>0 \). Solve the inequality by following steps: - step0: Solve for \(y\): \(\frac{3y+2}{2}-\frac{y-6}{3}>0\) - step1: Multiply both sides: \(\left(\frac{3y+2}{2}-\frac{y-6}{3}\right)\times 2\times 3>0\times 2\times 3\) - step2: Multiply the terms: \(9y+6-2y+12>0\) - step3: Simplify: \(7y+18>0\) - step4: Move the constant to the right side: \(7y>0-18\) - step5: Remove 0: \(7y>-18\) - step6: Divide both sides: \(\frac{7y}{7}>\frac{-18}{7}\) - step7: Divide the numbers: \(y>-\frac{18}{7}\) The solution to the inequality \( \frac{3y+2}{2}-\frac{y-6}{3}>0 \) is \( y > -\frac{18}{7} \).