1. Solve the inequality: \( \frac{y+3}{5} \geq \frac{y+2}{3}+2 \)

Solve the equation \( \frac{y+3}{5} \geq \frac{y+2}{3}+2 \). Solve the inequality by following steps: - step0: Solve for \(y\): \(\frac{y+3}{5}\geq \frac{y+2}{3}+2\) - step1: Multiply both sides: \(\frac{y+3}{5}\times 15\geq \left(\frac{y+2}{3}+2\right)\times 15\) - step2: Multiply the terms: \(3y+9\geq 5y+10+30\) - step3: Simplify: \(3y+9\geq 5y+40\) - step4: Move the expression to the left side: \(3y-5y\geq 40-9\) - step5: Add and subtract: \(-2y\geq 40-9\) - step6: Add and subtract: \(-2y\geq 31\) - step7: Change the signs: \(2y\leq -31\) - step8: Divide both sides: \(\frac{2y}{2}\leq \frac{-31}{2}\) - step9: Divide the numbers: \(y\leq -\frac{31}{2}\) The solution to the inequality \( \frac{y+3}{5} \geq \frac{y+2}{3}+2 \) is \( y \leq -\frac{31}{2} \).