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

To solve the inequality \( \frac{3y + 2}{2} - \frac{y - 6}{3} > 0 \), we’ll first find a common denominator, which is 6: \[ \frac{3(3y + 2)}{6} - \frac{2(y - 6)}{6} > 0 \] Simplifying this, we get: \[ \frac{9y + 6 - 2y + 12}{6} > 0 \] Combining like terms: \[ \frac{7y + 18}{6} > 0 \] Now, we can multiply both sides by 6 (which is positive, so the direction of the inequality stays the same): \[ 7y + 18 > 0 \] Next, we isolate \( y \): \[ 7y > -18 \] Dividing by 7 gives us: \[ y > -\frac{18}{7} \] Thus, the solution to the inequality is: \[ y > -\frac{18}{7} \] This means any value of \( y \) greater than \(-\frac{18}{7}\) will satisfy the inequality!