To solve the inequality $5y + 9 \leq 4$:

1. Subtract 9 from both sides of the inequality to isolate the term with $y$ on one side: $5y + 9 - 9 \leq 4 - 9$ This simplifies to: $5y \leq -5$

2. Divide both sides by 5 to solve for $y$: $y \leq \frac{-5}{5}$ Simplifying this gives: $y \leq -1$

So the solution to the inequality is $y \leq -1$.

Would you like more details on this, or do you have any further questions?

Here are five related questions to further explore this topic:

1. How would you graph the solution $y \leq -1$ on a number line?
2. How does the solution change if the inequality were $5y + 9 \geq 4$ instead?
3. What would happen if the inequality were $5y + 9 < 4$ instead of $\leq$?
4. How do you solve an inequality that involves division by a negative number?
5. How can you verify the solution to an inequality?

Tip: When solving inequalities, if you multiply or divide both sides by a negative number, remember to reverse the inequality sign.